因式分解(x^2+2x+2)^2+4(3x^2+7x+3)(2x^2+5x+1)

题目

因式分解(x^2+2x+2)^2+4(3x^2+7x+3)(2x^2+5x+1)

答案

设(x+1)^2=y,那么原式整理后=[(x+1)^2+1]^2+4[3(x+1)^2+x][2(x+1)^2+(x-1)]=(y+1)^2+4(3y+x)[2y+(x-1)]=y^2+2y+1+4[6y^2+(5x-3)y+x(x-1)]=25y^2+(20x-10)y+4x^2-4x+1=(5y)^2+10(2x-1)y+(2x-1)^2=[5y+(2x-1)]^2=[5(x+...