分解因式（高级）（1-7t-7t²-3t³）（1-2t-2t²-t³）-（t+1）ⁿn=6找到了求分送设t+t^2=m,t^3=n，（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-(t+1)^6=（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-[(t+1)^3]^2=(1-7m-3n)(1-2m-n)-[t^3+3t

Question

分解因式（高级）
（1-7t-7t²-3t³）（1-2t-2t²-t³）-（t+1）ⁿ
n=6
找到了
求分送
设t+t^2=m,t^3=n，
（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-(t+1)^6
=（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-[(t+1)^3]^2
=(1-7m-3n)(1-2m-n)-[t^3+3t^2+3t+]^2
=(1-7m-3n)(1-2m-n)-(3m+n+1)^2
=(5m+2n)(m+n-3)
=(2t^2+5t+5)t(t-1)(t^2+2t+3)

Answer 1

设t+t^2=m,t^3=n,（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-(t+1)^6=（1-7t-7t^2-3t^3)(1-2t-2t^2-t^3)-[(t+1)^3]^2=(1-7m-3n)(1-2m-n)-[t^3+3t^2+3t+]^2=(1-7m-3n)(1-2m-n)-(3m+n+1)^2 =(5m+2n)(m+n-3) =(2t^2+5t+5)t(t-1)(t^2+2t+3)