120:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Factorización y fracciones algebraicas:@0.073089:0.043661:0.408833:0.043661:0.408833:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.1 Trinomio cuadrado perfecto:@0.293660:0.231357:0.541273:0.231357:0.541273:0.214410:0.293660:0.214410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una expresión algebraica es un cuadrado perfecto cuando es el producto de dos factores :@0.293660:0.258720:0.931392:0.258720:0.931392:0.242286:0.293660:0.242286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iguales. Por ejemplo, 64  es cuadrado perfecto de 8 ; y 25  es cuadrado perfecto de 5 .:@0.293660:0.275362:0.926917:0.275362:0.926917:0.258928:0.293660:0.258928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.462050:0.275362:0.471309:0.275362:0.471309:0.258956:0.462050:0.258956:0.000000
2:@0.471215:0.269298:0.476452:0.269298:0.476452:0.259717:0.471215:0.259717:0.000000
a:@0.667600:0.275362:0.676859:0.275362:0.676859:0.258956:0.667600:0.258956:0.000000
x:@0.712606:0.275362:0.720061:0.275362:0.720061:0.258956:0.712606:0.258956:0.000000
2:@0.719965:0.269298:0.725202:0.269298:0.725202:0.259717:0.719965:0.259717:0.000000
x:@0.916351:0.275362:0.923806:0.275362:0.923806:0.258956:0.916351:0.258956:0.000000
En este tema, analizaremos la factorización de trinomios cuadrados perfectos.:@0.293670:0.306302:0.854585:0.306302:0.854585:0.289868:0.293670:0.289868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el diseño de la lámina de impresión radiográfica de la imagen, se ha usado la expresión :@0.293670:0.337242:0.930730:0.337242:0.930730:0.320808:0.293670:0.320808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9    6      para expresar su área, ¿es correcto decir que la placa es cuadrada?:@0.293670:0.353884:0.878109:0.353877:0.878109:0.337443:0.293670:0.337450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.302579:0.353884:0.310034:0.353884:0.310034:0.337477:0.302579:0.337477:0.000000
2:@0.309951:0.347813:0.315187:0.347813:0.315187:0.338232:0.309951:0.338232:0.000000
1:@0.319097:0.353323:0.334431:0.353323:0.334431:0.339607:0.319097:0.339607:0.000000
xy:@0.347187:0.353877:0.362244:0.353877:0.362244:0.337471:0.347187:0.337471:0.000000:0.000000
1:@0.366146:0.353323:0.381479:0.353323:0.381479:0.339607:0.366146:0.339607:0.000000
y:@0.385345:0.353877:0.392818:0.353877:0.392818:0.337471:0.385345:0.337471:0.000000
2:@0.392733:0.347813:0.397970:0.347813:0.397970:0.338232:0.392733:0.338232:0.000000
Dado que el área del cuadrado se obtiene al elevar su lado al cuadrado, debemos :@0.293663:0.384817:0.930748:0.384817:0.930748:0.368383:0.293663:0.368383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar la expresión que representa el área que resulta de esta operación. Para ello, :@0.293663:0.401459:0.930534:0.401459:0.930534:0.385025:0.293663:0.385025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vamos a conceptualizar lo que es un trinomio cuadrado perfecto.:@0.293663:0.418101:0.766502:0.418101:0.766502:0.401667:0.293663:0.401667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un trinomio cuadrado perfecto (TCP) es un polinomio ordenado en relación con una :@0.305401:0.453557:0.922791:0.453557:0.922791:0.437123:0.305401:0.437123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable; es cuadrado perfecto cuando el primer y tercer término son cuadrados :@0.305401:0.470199:0.921968:0.470199:0.921968:0.453765:0.305401:0.453765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
perfectos (o tienen la raíz cuadrada exacta) y positivos. Además, el segundo término :@0.305401:0.486840:0.922782:0.486840:0.922782:0.470407:0.305401:0.470407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivale al doble del producto de estas raíces cuadradas.:@0.305401:0.503482:0.717841:0.503482:0.717841:0.487048:0.305401:0.487048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.562863:0.520124:0.572122:0.520124:0.572122:0.503718:0.562863:0.503718:0.000000
2:@0.572063:0.514060:0.577300:0.514060:0.577300:0.504479:0.572063:0.504479:0.000000
   2  + :@0.577252:0.520124:0.646574:0.520124:0.646574:0.503690:0.577252:0.503690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.581210:0.519569:0.596543:0.519569:0.596543:0.505854:0.581210:0.505854:0.000000
ab:@0.609299:0.520124:0.627743:0.520124:0.627743:0.503718:0.609299:0.503718:0.000000:0.000000
b:@0.646482:0.520124:0.655741:0.520124:0.655741:0.503718:0.646482:0.503718:0.000000
2:@0.655666:0.514060:0.660902:0.514060:0.660902:0.504479:0.655666:0.504479:0.000000
Esta expresión se obtiene al desarrollar el cuadrado de un binomio. Por lo tanto: :@0.305401:0.536766:0.885279:0.536766:0.885279:0.520332:0.305401:0.520332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.520968:0.553408:0.530227:0.553408:0.530227:0.537002:0.520968:0.537002:0.000000
2:@0.530160:0.547344:0.535397:0.547344:0.535397:0.537763:0.530160:0.537763:0.000000
   2        (     ):@0.535351:0.553408:0.697651:0.553408:0.697651:0.536974:0.535351:0.536974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.539308:0.552853:0.554642:0.552853:0.554642:0.539137:0.539308:0.539137:0.000000
ab:@0.567398:0.553408:0.585842:0.553408:0.585842:0.537002:0.567398:0.537002:0.000000:0.000000
1:@0.589744:0.552853:0.605077:0.552853:0.605077:0.539137:0.589744:0.539137:0.000000
b:@0.608943:0.553408:0.618202:0.553408:0.618202:0.537002:0.608943:0.537002:0.000000
2:@0.618115:0.547344:0.623352:0.547344:0.623352:0.537763:0.618115:0.537763:0.000000
5:@0.627261:0.552853:0.642595:0.552853:0.642595:0.539137:0.627261:0.539137:0.000000
a:@0.651246:0.553408:0.660505:0.553408:0.660505:0.537002:0.651246:0.537002:0.000000
1:@0.664389:0.552853:0.679722:0.552853:0.679722:0.539137:0.664389:0.539137:0.000000
b:@0.683588:0.553408:0.692847:0.553408:0.692847:0.537002:0.683588:0.537002:0.000000
2:@0.697569:0.547344:0.702806:0.547344:0.702806:0.537763:0.697569:0.537763:0.000000
De acuerdo con esta información, determinamos si la expresión 9  + 6  +   es un :@0.293660:0.593371:0.930934:0.593371:0.930934:0.576937:0.293660:0.576937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.788134:0.593371:0.795589:0.593371:0.795589:0.576965:0.788134:0.576965:0.000000
2:@0.795678:0.587307:0.800915:0.587307:0.800915:0.577726:0.795678:0.577726:0.000000
xy:@0.831390:0.593371:0.846612:0.593371:0.846612:0.576965:0.831390:0.576965:0.000000:0.000000
y:@0.868038:0.593371:0.875512:0.593371:0.875512:0.576965:0.868038:0.576965:0.000000
2:@0.875599:0.587307:0.880836:0.587307:0.880836:0.577726:0.875599:0.577726:0.000000
trinomio cuadrado perfecto::@0.293655:0.610013:0.498749:0.610013:0.498749:0.593579:0.293655:0.593579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9    6    :@0.558131:0.640953:0.649891:0.640950:0.649891:0.624516:0.558131:0.624519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567040:0.640953:0.574495:0.640953:0.574495:0.624547:0.567040:0.624547:0.000000
2:@0.574421:0.634886:0.579658:0.634886:0.579658:0.625305:0.574421:0.625305:0.000000
1:@0.583569:0.640395:0.598903:0.640395:0.598903:0.626680:0.583569:0.626680:0.000000
xy:@0.611659:0.640950:0.626716:0.640950:0.626716:0.624544:0.611659:0.624544:0.000000:0.000000
1:@0.630618:0.640395:0.645952:0.640395:0.645952:0.626680:0.630618:0.626680:0.000000
y:@0.649817:0.640950:0.657290:0.640950:0.657290:0.624544:0.649817:0.624544:0.000000
2:@0.657203:0.634886:0.662440:0.634886:0.662440:0.625305:0.657203:0.625305:0.000000
3      :@0.559775:0.671888:0.639056:0.671888:0.639056:0.655454:0.559775:0.655454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568685:0.671888:0.576140:0.671888:0.576140:0.655482:0.568685:0.655482:0.000000
y:@0.653323:0.671888:0.660796:0.671888:0.660796:0.655482:0.653323:0.655482:0.000000
2(3 ):@0.589192:0.702828:0.624055:0.702828:0.624055:0.686394:0.589192:0.686394:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.611796:0.702828:0.631455:0.702828:0.631455:0.686421:0.611796:0.686421:0.000000:0.000000:0.000000
6:@0.598304:0.733767:0.607286:0.733767:0.607286:0.717334:0.598304:0.717334:0.000000
xy:@0.607213:0.733767:0.622270:0.733767:0.622270:0.717361:0.607213:0.717361:0.000000:0.000000
Regla para factorizar un trinomio cuadrado perfecto: se extrae la raíz cuadrada del primer :@0.293663:0.764707:0.931326:0.764707:0.931326:0.748274:0.293663:0.748274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y tercer término del trinomio y se separan estas raíces por el signo del segundo término. :@0.293663:0.781349:0.931374:0.781349:0.931374:0.764915:0.293663:0.764915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El binomio ya formado, que es la raíz cuadrada del trinomio, se multiplica por sí mismo o :@0.293663:0.797991:0.931339:0.797991:0.931339:0.781557:0.293663:0.781557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se eleva al cuadrado.:@0.293663:0.814633:0.443651:0.814633:0.443651:0.798199:0.293663:0.798199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9    6        (3     ):@0.515747:0.845573:0.699676:0.845560:0.699676:0.829126:0.515747:0.829139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.524656:0.845573:0.532111:0.845573:0.532111:0.829167:0.524656:0.829167:0.000000
2:@0.532037:0.839496:0.537274:0.839496:0.537274:0.829915:0.532037:0.829915:0.000000
1:@0.541186:0.845006:0.556519:0.845006:0.556519:0.831290:0.541186:0.831290:0.000000
xy:@0.569275:0.845560:0.584332:0.845560:0.584332:0.829154:0.569275:0.829154:0.000000:0.000000
1:@0.588235:0.845006:0.603568:0.845006:0.603568:0.831290:0.588235:0.831290:0.000000
y:@0.607434:0.845560:0.614907:0.845560:0.614907:0.829154:0.607434:0.829154:0.000000
2:@0.614820:0.839496:0.620057:0.839496:0.620057:0.829915:0.614820:0.829915:0.000000
5:@0.623967:0.845006:0.639300:0.845006:0.639300:0.831290:0.623967:0.831290:0.000000
x:@0.656860:0.845560:0.664315:0.845560:0.664315:0.829154:0.656860:0.829154:0.000000
1:@0.668199:0.845006:0.683532:0.845006:0.683532:0.831290:0.668199:0.831290:0.000000
y:@0.687398:0.845560:0.694871:0.845560:0.694871:0.829154:0.687398:0.829154:0.000000
2:@0.699587:0.839496:0.704824:0.839496:0.704824:0.829915:0.699587:0.829915:0.000000
El resultado obtenido nos permite deducir que la forma de la lámina de impresión :@0.293660:0.876496:0.931190:0.876496:0.931190:0.860063:0.293660:0.860063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
radiográfica es la de un cuadrado cuyo lado queda representado por la expresión 3x + y. :@0.293660:0.893138:0.931356:0.893138:0.931356:0.876704:0.293660:0.876704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 3. Factorización de trinomios:@0.073089:0.098522:0.589158:0.098522:0.589158:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desarrolla los siguientes binomios en tu cuaderno::@0.293660:0.162485:0.659394:0.162485:0.659394:0.146051:0.293660:0.146051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(     )  :@0.353907:0.188667:0.410655:0.188667:0.410655:0.172233:0.353907:0.172233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.358700:0.188667:0.366155:0.188667:0.366155:0.172261:0.358700:0.172261:0.000000
1:@0.370039:0.188112:0.385372:0.188112:0.385372:0.174396:0.370039:0.174396:0.000000
y:@0.389237:0.188667:0.396711:0.188667:0.396711:0.172261:0.389237:0.172261:0.000000
2:@0.401435:0.182603:0.406671:0.182603:0.406671:0.173022:0.401435:0.173022:0.000000
5:@0.410581:0.188112:0.425915:0.188112:0.425915:0.174396:0.410581:0.174396:0.000000
2    :@0.537479:0.188667:0.578797:0.188667:0.578797:0.172233:0.537479:0.172233:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.546382:0.188667:0.555641:0.188667:0.555641:0.172261:0.546382:0.172261:0.000000
1:@0.559524:0.188112:0.574858:0.188112:0.574858:0.174396:0.559524:0.174396:0.000000
1:@0.581772:0.181665:0.590755:0.181665:0.590755:0.165231:0.581772:0.165231:0.000000
3:@0.581772:0.195644:0.590755:0.195644:0.590755:0.179210:0.581772:0.179210:0.000000
b:@0.593737:0.188668:0.602996:0.188668:0.602996:0.172262:0.593737:0.172262:0.000000
2:@0.605774:0.173778:0.611010:0.173778:0.611010:0.164197:0.605774:0.164197:0.000000
 :@0.610963:0.188667:0.614994:0.188667:0.614994:0.172233:0.610963:0.172233:0.000000
5:@0.614920:0.188112:0.630253:0.188112:0.630253:0.174396:0.614920:0.174396:0.000000
x:@0.119867:0.177328:0.126643:0.177239:0.126298:0.162327:0.119521:0.162416:0.000000
2:@0.126455:0.171728:0.131215:0.171665:0.131013:0.162957:0.126253:0.163019:0.000000
1:@0.131288:0.176673:0.145226:0.176490:0.144937:0.164023:0.131000:0.164206:0.000000
2:@0.145154:0.176995:0.153319:0.176888:0.152973:0.161950:0.144808:0.162057:0.000000
ab b:@0.153252:0.176888:0.192236:0.176376:0.191890:0.161463:0.152906:0.161976:0.000000:0.000000:0.000000:0.000000
1:@0.169955:0.176164:0.183892:0.175981:0.183603:0.163514:0.169666:0.163698:0.000000
2:@0.192038:0.170865:0.196798:0.170803:0.196596:0.162094:0.191836:0.162157:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En diseño y construcción, el :@0.078672:0.472160:0.261071:0.472160:0.261071:0.457221:0.078672:0.457221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trinomio cuadrado perfecto :@0.078672:0.487289:0.261759:0.487289:0.261759:0.472349:0.078672:0.472349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se utiliza para calcular áreas :@0.078672:0.502418:0.258203:0.502418:0.258203:0.487478:0.078672:0.487478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de espacios cuadrados o :@0.078672:0.517547:0.241426:0.517547:0.241426:0.502607:0.078672:0.502607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectangulares con precisión, :@0.078672:0.532676:0.262735:0.532676:0.262735:0.517736:0.078672:0.517736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asegurar dimensiones y :@0.078672:0.547805:0.234883:0.547805:0.234883:0.532865:0.078672:0.532865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporciones exactas en :@0.078672:0.562934:0.240104:0.562934:0.240104:0.547994:0.078672:0.547994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elementos arquitectónicos, :@0.078672:0.578063:0.257301:0.578063:0.257301:0.563123:0.078672:0.563123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y optimizar el diseño de :@0.078672:0.593192:0.235971:0.593192:0.235971:0.578252:0.078672:0.578252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interiores para maximizar :@0.078672:0.608321:0.244068:0.608321:0.244068:0.593381:0.078672:0.593381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el uso del espacio. Este :@0.078672:0.623450:0.228947:0.623450:0.228947:0.608510:0.078672:0.608510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enfoque integra aspectos :@0.078672:0.638579:0.246648:0.638579:0.246648:0.623639:0.078672:0.623639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estéticos, funcionales y :@0.078672:0.653708:0.229751:0.653708:0.229751:0.638768:0.078672:0.638768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
técnicos, que facilitan :@0.078672:0.668837:0.220746:0.668837:0.220746:0.653897:0.078672:0.653897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la creación de edificios :@0.078672:0.683966:0.227764:0.683966:0.227764:0.669026:0.078672:0.669026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y espacios habitables y :@0.078672:0.699094:0.229411:0.699094:0.229411:0.684155:0.078672:0.684155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eficientes.:@0.078672:0.714223:0.142517:0.714223:0.142517:0.699284:0.078672:0.699284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078672:0.412540:0.231058:0.412540:0.231058:0.397133:0.078672:0.397133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y :@0.078672:0.427669:0.171582:0.427669:0.171582:0.412729:0.078672:0.412729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
arquitectura:@0.078672:0.442798:0.159142:0.442798:0.159142:0.427858:0.078672:0.427858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 8 (Ev. 4) Reconoce y representa relaciones numéricas mediante expresiones algebraicas y encuentra el conjunto de variación de :@0.218863:0.961846:0.919305:0.961846:0.919305:0.949894:0.218863:0.949894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una variable en función del contexto.:@0.218863:0.973949:0.414837:0.973949:0.414837:0.961997:0.218863:0.961997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000