Solución
desarrollar (164x+165y+163z+164u)4
Solución
409616x4+16u4+16x2u2+25x2y2+9x2z2+32x3u+32xu3+16u2x2+25u2y2+9u2z2+40x3y+24x3z+40yu3+24zu3+125xy3+125y3u+27xz3+27z3u+50xy2u+18xz2u+40x2yu+24x2zu+40xyu2+24xzu2+225xy2z+225y2zu+135xyz2+135yz2u+65536625y4+400y2x2+400y2u2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2u2+225z2y2+480x2yz+480yzu2+5125x3y+3x3z+5yu3+3zu3+25xyu2+15xzu2+25x2yu+15x2zu+204825y2x2+25y2u2+9z2x2+9z2u2+25x2y2+9x2z2+25u2y2+9u2z2+75x2yz+75yzu2+125xy2u+45xz2u+180xyzu+128(x2u+xu2)x+(x2u+xu2)u+327685(75y2z+45yz2)y+3(75y2z+45yz2)z
Pasos de solución
(164x+165y+163z+164u)4
Simplificar (164x+165y+163z+164u)4:(164x+165y+163z+164u)(164x+165y+163z+164u)(164x+165y+163z+164u)(164x+165y+163z+164u)
=(164x+165y+163z+164u)(164x+165y+163z+164u)(164x+165y+163z+164u)(164x+165y+163z+164u)
Desarrollar (164x+165y+163z+164u)(164x+165y+163z+164u):25616x2+16u2+25y2+9z2+325xy+3xz+5yu+3zu+8xu+12815yz
=(25616x2+16u2+25y2+9z2+325xy+3xz+5yu+3zu+8xu+12815yz)(164x+165y+163z+164u)(164x+165y+163z+164u)
Desarrollar (25616x2+16u2+25y2+9z2+325xy+3xz+5yu+3zu+8xu+12815yz)(164x+165y+163z+164u):1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu+32x2u+xu2+204875y2z+45yz2
=(1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu+32x2u+xu2+204875y2z+45yz2)(164x+165y+163z+164u)
Aplicar la siguiente regla de productos notables=1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u164x+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u165y+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u163z+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u164u+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z164x+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z165y+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z163z+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z164u+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu164x+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu165y+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu163z+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu164u+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu164x+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu165y+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu163z+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu164u+32x2u+xu2164x+32x2u+xu2165y+32x2u+xu2163z+32x2u+xu2164u+204875y2z+45yz2164x+204875y2z+45yz2165y+204875y2z+45yz2163z+204875y2z+45yz2164u
Simplificar 1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u164x+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u165y+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u163z+1024(16x2+16u2+25y2+9z2)x+(16x2+16u2+25y2+9z2)u164u+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z164x+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z165y+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z163z+40965(16x2+16u2+25y2+9z2)y+3(16x2+16u2+25y2+9z2)z164u+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu164x+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu165y+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu163z+1285x2y+3x2z+5yu2+3zu2+15xyu+9xzu164u+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu164x+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu165y+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu163z+51225xy2+25y2u+9xz2+9z2u+45xyz+45yzu164u+32x2u+xu2164x+32x2u+xu2165y+32x2u+xu2163z+32x2u+xu2164u+204875y2z+45yz2164x+204875y2z+45yz2165y+204875y2z+45yz2163z+204875y2z+45yz2164u:409616x4+16u4+16x2u2+25x2y2+9x2z2+32x3u+32xu3+16u2x2+25u2y2+9u2z2+40x3y+24x3z+40yu3+24zu3+125xy3+125y3u+27xz3+27z3u+50xy2u+18xz2u+40x2yu+24x2zu+40xyu2+24xzu2+225xy2z+225y2zu+135xyz2+135yz2u+65536625y4+400y2x2+400y2u2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2u2+225z2y2+480x2yz+480yzu2+5125x3y+3x3z+5yu3+3zu3+25xyu2+15xzu2+25x2yu+15x2zu+204825y2x2+25y2u2+9z2x2+9z2u2+25x2y2+9x2z2+25u2y2+9u2z2+75x2yz+75yzu2+125xy2u+45xz2u+180xyzu+128(x2u+xu2)x+(x2u+xu2)u+327685(75y2z+45yz2)y+3(75y2z+45yz2)z
=409616x4+16u4+16x2u2+25x2y2+9x2z2+32x3u+32xu3+16u2x2+25u2y2+9u2z2+40x3y+24x3z+40yu3+24zu3+125xy3+125y3u+27xz3+27z3u+50xy2u+18xz2u+40x2yu+24x2zu+40xyu2+24xzu2+225xy2z+225y2zu+135xyz2+135yz2u+65536625y4+400y2x2+400y2u2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2u2+225z2y2+480x2yz+480yzu2+5125x3y+3x3z+5yu3+3zu3+25xyu2+15xzu2+25x2yu+15x2zu+204825y2x2+25y2u2+9z2x2+9z2u2+25x2y2+9x2z2+25u2y2+9u2z2+75x2yz+75yzu2+125xy2u+45xz2u+180xyzu+128(x2u+xu2)x+(x2u+xu2)u+327685(75y2z+45yz2)y+3(75y2z+45yz2)z