95:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El producto notable de dos binomios con un término común, se resuelve así: :@0.080653:0.142792:0.641244:0.142792:0.641244:0.126358:0.080653:0.126358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) ( ) ( ) :@0.256963:0.159434:0.504094:0.159434:0.504094:0.143000:0.256963:0.143000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.261767:0.159434:0.269222:0.159434:0.269222:0.143028:0.261767:0.143028:0.000000 1:@0.273106:0.158879:0.288439:0.158879:0.288439:0.145163:0.273106:0.145163:0.000000 a x:@0.292305:0.159434:0.322493:0.159434:0.322493:0.143028:0.292305:0.143028:0.000000:0.000000:0.000000 1:@0.326377:0.158879:0.341710:0.158879:0.341710:0.145163:0.326377:0.145163:0.000000 b:@0.345575:0.159434:0.354834:0.159434:0.354834:0.143028:0.345575:0.143028:0.000000 5:@0.363504:0.158879:0.378837:0.158879:0.378837:0.145163:0.363504:0.145163:0.000000 x:@0.382703:0.159434:0.390158:0.159434:0.390158:0.143028:0.382703:0.143028:0.000000 2:@0.390081:0.153370:0.395318:0.153370:0.395318:0.143789:0.390081:0.143789:0.000000 1:@0.399227:0.158879:0.414561:0.158879:0.414561:0.145163:0.399227:0.145163:0.000000 a:@0.423212:0.159434:0.432471:0.159434:0.432471:0.143028:0.423212:0.143028:0.000000 1:@0.436355:0.158879:0.451688:0.158879:0.451688:0.145163:0.436355:0.145163:0.000000 b x:@0.455554:0.159434:0.480937:0.159434:0.480937:0.143028:0.455554:0.143028:0.000000:0.000000:0.000000 1:@0.484821:0.158879:0.500154:0.158879:0.500154:0.145163:0.484821:0.145163:0.000000 ab:@0.504020:0.159434:0.522464:0.159434:0.522464:0.143028:0.504020:0.143028:0.000000:0.000000 Ejemplo 3:@0.073088:0.197086:0.148870:0.197086:0.148870:0.180416:0.073088:0.180416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Obtén los productos notables.:@0.073088:0.228026:0.292706:0.228026:0.292706:0.211592:0.073088:0.211592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. (2 3)(2 4):@0.073089:0.258960:0.219238:0.258960:0.219238:0.242526:0.073089:0.242526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.116985:0.258960:0.124440:0.258960:0.124440:0.242553:0.116985:0.242553:0.000000 1:@0.128324:0.258405:0.143658:0.258405:0.143658:0.244689:0.128324:0.244689:0.000000 x:@0.174913:0.258960:0.182368:0.258960:0.182368:0.242553:0.174913:0.242553:0.000000 2:@0.186252:0.258405:0.201585:0.258405:0.201585:0.244689:0.186252:0.244689:0.000000 b. :@0.073089:0.294458:0.089987:0.294458:0.089987:0.278025:0.073089:0.278025:0.000000:0.000000:0.000000 2:@0.109427:0.288216:0.118410:0.288216:0.118410:0.271783:0.109427:0.271783:0.000000 5:@0.109427:0.302196:0.118410:0.302196:0.118410:0.285762:0.109427:0.285762:0.000000 m:@0.121171:0.294457:0.135787:0.294457:0.135787:0.278051:0.121171:0.278051:0.000000 2:@0.135713:0.293902:0.151046:0.293902:0.151046:0.280187:0.135713:0.280187:0.000000 3:@0.150954:0.294457:0.159937:0.294457:0.159937:0.278023:0.150954:0.278023:0.000000 n:@0.159863:0.294457:0.169361:0.294457:0.169361:0.278051:0.159863:0.278051:0.000000 :@0.172591:0.282089:0.174941:0.282089:0.174941:0.272509:0.172591:0.272509:0.000000 2:@0.181031:0.288216:0.190014:0.288216:0.190014:0.271783:0.181031:0.271783:0.000000 5:@0.181031:0.302196:0.190014:0.302196:0.190014:0.285762:0.181031:0.285762:0.000000 x n:@0.192775:0.294457:0.224896:0.294457:0.224896:0.278051:0.192775:0.278051:0.000000:0.000000:0.000000 2:@0.200156:0.293902:0.215490:0.293902:0.215490:0.280187:0.200156:0.280187:0.000000 Solución:@0.073089:0.325395:0.139222:0.325395:0.139222:0.308725:0.073089:0.308725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. (:@0.073089:0.356332:0.108168:0.356332:0.108168:0.339898:0.073089:0.339898:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.108095:0.356332:0.115550:0.356332:0.115550:0.339926:0.108095:0.339926:0.000000 1:@0.115476:0.355777:0.130809:0.355777:0.130809:0.342062:0.115476:0.342062:0.000000 3)(:@0.130717:0.356332:0.149309:0.356332:0.149309:0.339898:0.130717:0.339898:0.000000:0.000000:0.000000 x:@0.149217:0.356332:0.156671:0.356332:0.156671:0.339926:0.149217:0.339926:0.000000 2 5:@0.156598:0.355777:0.200867:0.355777:0.200867:0.342062:0.156598:0.342062:0.000000:0.000000:0.000000 4) ( ):@0.171839:0.356332:0.217839:0.356332:0.217839:0.339898:0.171839:0.339898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.205580:0.356332:0.213035:0.356332:0.213035:0.339926:0.205580:0.339926:0.000000 2:@0.217769:0.350268:0.223006:0.350268:0.223006:0.340687:0.217769:0.340687:0.000000 1 2:@0.222958:0.355777:0.267227:0.355777:0.267227:0.342062:0.222958:0.342062:0.000000:0.000000:0.000000 (3 4):@0.238199:0.356332:0.280922:0.356332:0.280922:0.339898:0.238199:0.339898:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.280830:0.356332:0.288285:0.356332:0.288285:0.339926:0.280830:0.339926:0.000000 1:@0.288212:0.355777:0.303545:0.355777:0.303545:0.342062:0.288212:0.342062:0.000000 (3)( 4):@0.303453:0.356332:0.355766:0.356332:0.355766:0.339898:0.303453:0.339898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5 2 2:@0.326738:0.355777:0.421480:0.355777:0.421480:0.342062:0.326738:0.342062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.370915:0.356332:0.378370:0.356332:0.378370:0.339926:0.370915:0.339926:0.000000 2:@0.378333:0.350268:0.383570:0.350268:0.383570:0.340687:0.378333:0.340687:0.000000 x:@0.398766:0.356332:0.406220:0.356332:0.406220:0.339926:0.398766:0.339926:0.000000 12:@0.421388:0.356332:0.439280:0.356332:0.439280:0.339898:0.421388:0.339898:0.000000:0.000000 b. (:@0.073089:0.387268:0.108168:0.387268:0.108168:0.370834:0.073089:0.370834:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.108095:0.387268:0.122710:0.387268:0.122710:0.370862:0.108095:0.370862:0.000000 1:@0.122636:0.386713:0.137970:0.386713:0.137970:0.372998:0.122636:0.372998:0.000000 3 )(:@0.137878:0.387268:0.165894:0.387268:0.165894:0.370834:0.137878:0.370834:0.000000:0.000000:0.000000:0.000000 n m n:@0.146787:0.387268:0.205083:0.387268:0.205083:0.370862:0.146787:0.370862:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.180343:0.386713:0.225146:0.386713:0.225146:0.372998:0.180343:0.372998:0.000000:0.000000:0.000000 ) ( ):@0.205009:0.387268:0.249278:0.387268:0.249278:0.370834:0.205009:0.370834:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.229859:0.387268:0.244474:0.387268:0.244474:0.370862:0.229859:0.370862:0.000000 2:@0.249212:0.381204:0.254448:0.381204:0.254448:0.371623:0.249212:0.371623:0.000000 1:@0.254401:0.386713:0.269734:0.386713:0.269734:0.372998:0.254401:0.372998:0.000000 (3:@0.269642:0.387268:0.283429:0.387268:0.283429:0.370834:0.269642:0.370834:0.000000:0.000000 n n m:@0.283337:0.387268:0.336847:0.387268:0.336847:0.370862:0.283337:0.370862:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.292762:0.386713:0.308095:0.386713:0.308095:0.372998:0.292762:0.372998:0.000000 ):@0.317427:0.387268:0.322305:0.387268:0.322305:0.370834:0.317427:0.370834:0.000000 1:@0.336773:0.386713:0.352107:0.386713:0.352107:0.372998:0.336773:0.372998:0.000000 (3 )(:@0.352014:0.387268:0.384816:0.387268:0.384816:0.370834:0.352014:0.370834:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.365709:0.387268:0.375208:0.387268:0.375208:0.370862:0.365709:0.370862:0.000000 2 5:@0.384724:0.386713:0.429527:0.386713:0.429527:0.372998:0.384724:0.372998:0.000000:0.000000:0.000000 n:@0.399965:0.387268:0.409464:0.387268:0.409464:0.370862:0.399965:0.370862:0.000000 ):@0.409390:0.387268:0.414268:0.387268:0.414268:0.370834:0.409390:0.370834:0.000000 m:@0.429435:0.387268:0.444051:0.387268:0.444051:0.370862:0.429435:0.370862:0.000000 2:@0.444021:0.381204:0.449257:0.381204:0.449257:0.371623:0.444021:0.371623:0.000000 1:@0.449211:0.386713:0.464545:0.386713:0.464545:0.372998:0.449211:0.372998:0.000000 2:@0.464453:0.387268:0.473435:0.387268:0.473435:0.370834:0.464453:0.370834:0.000000 nm:@0.473362:0.387268:0.497402:0.387268:0.497402:0.370862:0.473362:0.370862:0.000000:0.000000 2:@0.497346:0.386713:0.512680:0.386713:0.512680:0.372998:0.497346:0.372998:0.000000 3:@0.512588:0.387268:0.521570:0.387268:0.521570:0.370834:0.512588:0.370834:0.000000 n:@0.521497:0.387268:0.530995:0.387268:0.530995:0.370862:0.521497:0.370862:0.000000 2:@0.530910:0.381204:0.536146:0.381204:0.536146:0.371623:0.530910:0.371623:0.000000 4.4 Binomio al cubo ( ):@0.073089:0.418206:0.285324:0.418206:0.285324:0.401259:0.073089:0.401259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.237245:0.418206:0.247185:0.418206:0.247185:0.401259:0.237245:0.401259:0.000000 1:@0.250848:0.417651:0.266181:0.417651:0.266181:0.403935:0.250848:0.403935:0.000000 b:@0.269826:0.418206:0.279858:0.418206:0.279858:0.401259:0.269826:0.401259:0.000000 3:@0.285256:0.412142:0.291008:0.412142:0.291008:0.402262:0.285256:0.402262:0.000000 Para obtener el resultado de un binomio al cubo, seguiremos estos pasos::@0.073089:0.449142:0.605677:0.449142:0.605677:0.432708:0.073089:0.432708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Descomponemos la potencia en dos factores: ( ) ( ):@0.073089:0.480079:0.550493:0.480079:0.550493:0.463645:0.073089:0.463645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.443825:0.480079:0.453084:0.480079:0.453084:0.463673:0.443825:0.463673:0.000000 1:@0.456967:0.479524:0.472301:0.479524:0.472301:0.465809:0.456967:0.465809:0.000000 b:@0.476166:0.480079:0.485425:0.480079:0.485425:0.463673:0.476166:0.463673:0.000000 2:@0.490154:0.474015:0.495391:0.474015:0.495391:0.464434:0.490154:0.464434:0.000000 a:@0.504089:0.480079:0.513347:0.480079:0.513347:0.463673:0.504089:0.463673:0.000000 1:@0.517231:0.479524:0.532565:0.479524:0.532565:0.465809:0.517231:0.465809:0.000000 b:@0.536430:0.480079:0.545689:0.480079:0.545689:0.463673:0.536430:0.463673:0.000000 2. Desarrollamos el binomio al cuadrado: ( 2 + )( ):@0.073089:0.511017:0.544427:0.511017:0.544427:0.494583:0.073089:0.494583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.390444:0.511017:0.399702:0.511017:0.399702:0.494610:0.390444:0.494610:0.000000 2:@0.399639:0.504953:0.404876:0.504953:0.404876:0.495372:0.399639:0.495372:0.000000 1:@0.408787:0.510462:0.424121:0.510462:0.424121:0.496746:0.408787:0.496746:0.000000 ab:@0.436877:0.511017:0.455321:0.511017:0.455321:0.494610:0.436877:0.494610:0.000000:0.000000 b a:@0.474060:0.511017:0.507281:0.511017:0.507281:0.494610:0.474060:0.494610:0.000000:0.000000:0.000000 2:@0.483243:0.504953:0.488480:0.504953:0.488480:0.495372:0.483243:0.495372:0.000000 1:@0.511165:0.510462:0.526498:0.510462:0.526498:0.496746:0.511165:0.496746:0.000000 b:@0.530364:0.511017:0.539623:0.511017:0.539623:0.494610:0.530364:0.494610:0.000000 3. Aplicamos la propiedad distributiva y multiplicamos: :@0.073089:0.541953:0.490910:0.541953:0.490910:0.525519:0.073089:0.525519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a :@0.103217:0.558595:0.139906:0.558595:0.139906:0.542161:0.103217:0.542161:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.111486:0.552531:0.116723:0.552531:0.116723:0.542950:0.111486:0.542950:0.000000 1:@0.120634:0.558040:0.135967:0.558040:0.135967:0.544324:0.120634:0.544324:0.000000 a b:@0.139832:0.558595:0.163461:0.558595:0.163461:0.542188:0.139832:0.542188:0.000000:0.000000:0.000000 2:@0.149011:0.552531:0.154248:0.552531:0.154248:0.542950:0.149011:0.542950:0.000000 2:@0.163387:0.558595:0.195526:0.558595:0.195526:0.542161:0.163387:0.542161:0.000000:0.000000:0.000000:0.000000 1:@0.167345:0.558040:0.182678:0.558040:0.182678:0.544324:0.167345:0.544324:0.000000 a b:@0.195434:0.558595:0.219079:0.558595:0.219079:0.542188:0.195434:0.542188:0.000000:0.000000:0.000000 2:@0.204631:0.552531:0.209868:0.552531:0.209868:0.542950:0.204631:0.542950:0.000000 2:@0.219005:0.558595:0.251144:0.558595:0.251144:0.542161:0.219005:0.542161:0.000000:0.000000:0.000000:0.000000 1:@0.222963:0.558040:0.238296:0.558040:0.238296:0.544324:0.222963:0.544324:0.000000 ab:@0.251052:0.558595:0.269496:0.558595:0.269496:0.542188:0.251052:0.542188:0.000000:0.000000 2:@0.269443:0.552531:0.274680:0.552531:0.274680:0.542950:0.269443:0.542950:0.000000 :@0.274632:0.558595:0.297862:0.558595:0.297862:0.542161:0.274632:0.542161:0.000000:0.000000:0.000000 1:@0.278590:0.558040:0.293923:0.558040:0.293923:0.544324:0.278590:0.544324:0.000000 ab:@0.297788:0.558595:0.316232:0.558595:0.316232:0.542188:0.297788:0.542188:0.000000:0.000000 2:@0.316160:0.552531:0.321397:0.552531:0.321397:0.542950:0.316160:0.542950:0.000000 :@0.321350:0.558595:0.344580:0.558595:0.344580:0.542161:0.321350:0.542161:0.000000:0.000000:0.000000 1:@0.325307:0.558040:0.340640:0.558040:0.340640:0.544324:0.325307:0.544324:0.000000 b:@0.344506:0.558595:0.353765:0.558595:0.353765:0.542188:0.344506:0.542188:0.000000 3:@0.353685:0.552531:0.358921:0.552531:0.358921:0.542950:0.353685:0.542950:0.000000 4. Reducimos términos semejantes: 3:@0.073089:0.589532:0.393344:0.589532:0.393344:0.573098:0.073089:0.573098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.346818:0.589532:0.356077:0.589532:0.356077:0.573126:0.346818:0.573126:0.000000 3:@0.356016:0.583468:0.361252:0.583468:0.361252:0.573887:0.356016:0.573887:0.000000 1:@0.365162:0.588977:0.380496:0.588977:0.380496:0.575262:0.365162:0.575262:0.000000 a b:@0.393252:0.589532:0.416892:0.589532:0.416892:0.573126:0.393252:0.573126:0.000000:0.000000:0.000000 2:@0.402442:0.583468:0.407679:0.583468:0.407679:0.573887:0.402442:0.573887:0.000000 3:@0.416818:0.589532:0.448957:0.589532:0.448957:0.573098:0.416818:0.573098:0.000000:0.000000:0.000000:0.000000 1:@0.420776:0.588977:0.436109:0.588977:0.436109:0.575262:0.420776:0.575262:0.000000 ab:@0.448865:0.589532:0.467309:0.589532:0.467309:0.573126:0.448865:0.573126:0.000000:0.000000 2:@0.467254:0.583468:0.472491:0.583468:0.472491:0.573887:0.467254:0.573887:0.000000 :@0.472445:0.589532:0.495675:0.589532:0.495675:0.573098:0.472445:0.573098:0.000000:0.000000:0.000000 1:@0.476402:0.588977:0.491736:0.588977:0.491736:0.575262:0.476402:0.575262:0.000000 b:@0.495601:0.589532:0.504860:0.589532:0.504860:0.573126:0.495601:0.573126:0.000000 3:@0.504780:0.583468:0.510016:0.583468:0.510016:0.573887:0.504780:0.573887:0.000000 Un binomio al cubo es igual al cubo del primer término más el triple del producto del :@0.080653:0.622064:0.703173:0.622064:0.703173:0.605630:0.080653:0.605630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuadrado del primer término con el segundo término, más el triple del primer término :@0.080653:0.638706:0.702430:0.638706:0.702430:0.622272:0.080653:0.622272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con el cuadrado del segundo término y más el cubo del segundo término.:@0.080653:0.655348:0.620081:0.655348:0.620081:0.638914:0.080653:0.638914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si el binomio tiene signo negativo ( ) , los signos van alternados: :@0.080653:0.671990:0.584090:0.671990:0.584090:0.655556:0.080653:0.655556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.336587:0.671990:0.345846:0.671990:0.345846:0.655584:0.336587:0.655584:0.000000 2:@0.349730:0.671435:0.365063:0.671435:0.365063:0.657719:0.349730:0.657719:0.000000 b:@0.368929:0.671990:0.378188:0.671990:0.378188:0.655584:0.368929:0.655584:0.000000 3:@0.382919:0.665926:0.388155:0.665926:0.388155:0.656345:0.382919:0.656345:0.000000 a:@0.310705:0.688632:0.319964:0.688632:0.319964:0.672225:0.310705:0.672225:0.000000 3:@0.319906:0.682568:0.325142:0.682568:0.325142:0.672987:0.319906:0.672987:0.000000 3:@0.325096:0.688632:0.357235:0.688632:0.357235:0.672198:0.325096:0.672198:0.000000:0.000000:0.000000:0.000000 2:@0.329054:0.688077:0.344387:0.688077:0.344387:0.674361:0.329054:0.674361:0.000000 a b:@0.357143:0.688632:0.380782:0.688632:0.380782:0.672225:0.357143:0.672225:0.000000:0.000000:0.000000 2:@0.366332:0.682568:0.371569:0.682568:0.371569:0.672987:0.366332:0.672987:0.000000 3 :@0.380708:0.688632:0.454374:0.688632:0.454374:0.672198:0.380708:0.672198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.384666:0.688077:0.399999:0.688077:0.399999:0.674361:0.384666:0.674361:0.000000 ab:@0.412755:0.688632:0.431199:0.688632:0.431199:0.672225:0.412755:0.672225:0.000000:0.000000 2:@0.435101:0.688077:0.450435:0.688077:0.450435:0.674361:0.435101:0.674361:0.000000 b:@0.454300:0.688632:0.463559:0.688632:0.463559:0.672225:0.454300:0.672225:0.000000 3:@0.463480:0.682568:0.468717:0.682568:0.468717:0.672987:0.463480:0.672987:0.000000 Ejemplo 4:@0.073089:0.725803:0.148872:0.725803:0.148872:0.709134:0.073089:0.709134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resuelve :@0.073089:0.756743:0.141494:0.756743:0.141494:0.740309:0.073089:0.740309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.076385:0.792238:0.085367:0.792238:0.085367:0.775804:0.076385:0.775804:0.000000 x :@0.085287:0.792238:0.095982:0.792238:0.095982:0.775832:0.085287:0.775832:0.000000:0.000000 2 :@0.095926:0.791684:0.115769:0.791684:0.115769:0.777968:0.095926:0.777968:0.000000:0.000000 1:@0.118515:0.785996:0.127498:0.785996:0.127498:0.769563:0.118515:0.769563:0.000000 5:@0.118515:0.799975:0.127498:0.799975:0.127498:0.783542:0.118515:0.783542:0.000000 y:@0.130259:0.792237:0.137732:0.792237:0.137732:0.775831:0.130259:0.775831:0.000000 3:@0.140962:0.778610:0.146199:0.778610:0.146199:0.769029:0.140962:0.769029:0.000000 :@0.146198:0.792238:0.150229:0.792238:0.150229:0.775804:0.146198:0.775804:0.000000 Solución:@0.073084:0.823178:0.139218:0.823178:0.139218:0.806509:0.073084:0.806509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.076385:0.858673:0.085367:0.858673:0.085367:0.842239:0.076385:0.842239:0.000000 x :@0.085287:0.858673:0.095982:0.858673:0.095982:0.842267:0.085287:0.842267:0.000000:0.000000 2 :@0.095926:0.858119:0.115769:0.858119:0.115769:0.844403:0.095926:0.844403:0.000000:0.000000 1:@0.118515:0.852433:0.127498:0.852433:0.127498:0.835999:0.118515:0.835999:0.000000 5:@0.118515:0.866412:0.127498:0.866412:0.127498:0.849978:0.118515:0.849978:0.000000 y:@0.130259:0.858673:0.137732:0.858673:0.137732:0.842267:0.130259:0.842267:0.000000 3:@0.140962:0.845045:0.146199:0.845045:0.146199:0.835464:0.140962:0.835464:0.000000 (5 ) 3 (5 ) :@0.146151:0.858673:0.267520:0.858673:0.267520:0.842239:0.146151:0.842239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.150109:0.858119:0.165442:0.858119:0.165442:0.844403:0.150109:0.844403:0.000000 x:@0.183002:0.858673:0.190457:0.858673:0.190457:0.842267:0.183002:0.842267:0.000000 3:@0.195180:0.852609:0.200417:0.852609:0.200417:0.843028:0.195180:0.843028:0.000000 2:@0.204326:0.858119:0.219660:0.858119:0.219660:0.844403:0.204326:0.844403:0.000000 x:@0.246111:0.858673:0.253566:0.858673:0.253566:0.842267:0.246111:0.842267:0.000000 2:@0.258298:0.852609:0.263535:0.852609:0.263535:0.843028:0.258298:0.843028:0.000000 1:@0.273576:0.852433:0.282559:0.852433:0.282559:0.835999:0.273576:0.835999:0.000000 5:@0.273576:0.866412:0.282559:0.866412:0.282559:0.849978:0.273576:0.849978:0.000000 y:@0.285320:0.858673:0.292793:0.858673:0.292793:0.842267:0.285320:0.842267:0.000000 :@0.296023:0.845045:0.298373:0.845045:0.298373:0.835464:0.296023:0.835464:0.000000 1:@0.298326:0.858119:0.313659:0.858119:0.313659:0.844403:0.298326:0.844403:0.000000 3 (5 ) :@0.313567:0.858673:0.356327:0.858673:0.356327:0.842239:0.313567:0.842239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.340110:0.858673:0.347565:0.858673:0.347565:0.842267:0.340110:0.842267:0.000000 1:@0.362393:0.852433:0.371376:0.852433:0.371376:0.835999:0.362393:0.835999:0.000000 5:@0.362393:0.866412:0.371376:0.866412:0.371376:0.849978:0.362393:0.849978:0.000000 y:@0.374137:0.858673:0.381610:0.858673:0.381610:0.842267:0.374137:0.842267:0.000000 2:@0.384840:0.845045:0.390076:0.845045:0.390076:0.835464:0.384840:0.835464:0.000000 :@0.390029:0.858673:0.413259:0.858673:0.413259:0.842239:0.390029:0.842239:0.000000:0.000000:0.000000 2:@0.393986:0.858119:0.409320:0.858119:0.409320:0.844403:0.393986:0.844403:0.000000 1:@0.419308:0.852433:0.428291:0.852433:0.428291:0.835999:0.419308:0.835999:0.000000 5:@0.419308:0.866412:0.428291:0.866412:0.428291:0.849978:0.419308:0.849978:0.000000 y:@0.431052:0.858673:0.438525:0.858673:0.438525:0.842267:0.431052:0.842267:0.000000 3:@0.441755:0.845045:0.446992:0.845045:0.446992:0.835464:0.441755:0.835464:0.000000 5:@0.130010:0.893617:0.145344:0.893617:0.145344:0.879902:0.130010:0.879902:0.000000 125 15:@0.145252:0.894172:0.229536:0.894172:0.229536:0.877738:0.145252:0.877738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.175900:0.894172:0.183355:0.894172:0.183355:0.877766:0.175900:0.877766:0.000000 3:@0.183297:0.888108:0.188534:0.888108:0.188534:0.878527:0.183297:0.878527:0.000000 2:@0.192445:0.893617:0.207779:0.893617:0.207779:0.879902:0.192445:0.879902:0.000000 x y:@0.229444:0.894172:0.249486:0.894172:0.249486:0.877766:0.229444:0.877766:0.000000:0.000000:0.000000 2:@0.236822:0.888108:0.242059:0.888108:0.242059:0.878527:0.236822:0.878527:0.000000 :@0.249412:0.894172:0.253444:0.894172:0.253444:0.877738:0.249412:0.877738:0.000000 1:@0.253370:0.893617:0.268703:0.893617:0.268703:0.879902:0.253370:0.879902:0.000000 3:@0.271453:0.887930:0.280435:0.887930:0.280435:0.871496:0.271453:0.871496:0.000000 5:@0.271453:0.901909:0.280435:0.901909:0.280435:0.885475:0.271453:0.885475:0.000000 :@0.283196:0.894171:0.287228:0.894171:0.287228:0.877737:0.283196:0.877737:0.000000 xy:@0.287154:0.894171:0.302211:0.894171:0.302211:0.877765:0.287154:0.877765:0.000000:0.000000 2 :@0.302144:0.888108:0.309688:0.888108:0.309688:0.878527:0.302144:0.878527:0.000000:0.000000 2:@0.309638:0.893617:0.324971:0.893617:0.324971:0.879902:0.309638:0.879902:0.000000 :@0.324879:0.888108:0.327229:0.888108:0.327229:0.878527:0.324879:0.878527:0.000000 1:@0.338659:0.887930:0.347642:0.887930:0.347642:0.871496:0.338659:0.871496:0.000000 125:@0.329750:0.901909:0.356551:0.901909:0.356551:0.885475:0.329750:0.885475:0.000000:0.000000:0.000000 y:@0.359036:0.894171:0.366509:0.894171:0.366509:0.877765:0.359036:0.877765:0.000000 3:@0.366446:0.888108:0.371683:0.888108:0.371683:0.878527:0.366446:0.878527:0.000000 Representación :@0.740294:0.413465:0.846758:0.413465:0.846758:0.398525:0.740294:0.398525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 geométrica del cubo del :@0.740294:0.428594:0.906220:0.428594:0.906220:0.413654:0.740294:0.413654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 binomio ( ):@0.740294:0.443723:0.846637:0.443723:0.846637:0.428783:0.740294:0.428783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.804451:0.443723:0.812869:0.443723:0.812869:0.428808:0.804451:0.428808:0.000000 1:@0.816399:0.443219:0.830339:0.443219:0.830339:0.430750:0.816399:0.430750:0.000000 b:@0.833853:0.443723:0.842270:0.443723:0.842270:0.428808:0.833853:0.428808:0.000000 3:@0.846555:0.438210:0.851316:0.438210:0.851316:0.429500:0.846555:0.429500:0.000000 b:@0.779068:0.493435:0.788954:0.493435:0.788954:0.477445:0.779068:0.477445:0.000000 3:@0.788956:0.487535:0.794051:0.487535:0.794051:0.478213:0.788956:0.478213:0.000000 ab:@0.821978:0.493435:0.839996:0.493435:0.839996:0.477445:0.821978:0.477445:0.000000:0.000000 2:@0.839997:0.487535:0.845093:0.487535:0.845093:0.478213:0.839997:0.478213:0.000000 ab:@0.775711:0.526327:0.793729:0.526327:0.793729:0.510336:0.775711:0.510336:0.000000:0.000000 2:@0.793728:0.520427:0.798824:0.520427:0.798824:0.511104:0.793728:0.511104:0.000000 ab:@0.775709:0.600169:0.793727:0.600169:0.793727:0.584178:0.775709:0.584178:0.000000:0.000000 2:@0.793727:0.594269:0.798822:0.594269:0.798822:0.584946:0.793727:0.584946:0.000000 a b:@0.821978:0.526327:0.845092:0.526327:0.845092:0.510336:0.821978:0.510336:0.000000:0.000000:0.000000 2:@0.830109:0.520427:0.835205:0.520427:0.835205:0.511104:0.830109:0.511104:0.000000 a:@0.826572:0.634373:0.834703:0.634373:0.834703:0.618383:0.826572:0.618383:0.000000 3:@0.834711:0.628471:0.839807:0.628471:0.839807:0.619149:0.834711:0.619149:0.000000 a b:@0.773720:0.636902:0.796833:0.636902:0.796833:0.620911:0.773720:0.620911:0.000000:0.000000:0.000000 2:@0.781851:0.631002:0.786946:0.631002:0.786946:0.621679:0.781851:0.621679:0.000000 a b:@0.819490:0.600171:0.842605:0.600169:0.842605:0.584178:0.819490:0.584181:0.000000:0.000000:0.000000 2:@0.827623:0.594269:0.832718:0.594269:0.832718:0.584946:0.827623:0.584946:0.000000 Competencia :@0.740294:0.374024:0.848854:0.374024:0.848854:0.357077:0.740294:0.357077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.390666:0.837769:0.390666:0.837769:0.373719:0.740294:0.373719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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