Question

(x-y+2z)^2-(x-2y-3z)^2

因式分解

Answer 1

平方差
原式=[(x-y+2z)+(x-2y-3z)][(x-y+2z)-(x-2y-3z)]
=(2x-3y-z)(y+5z)

Answer 2

(x-y+2z)^2-(x-2y-3z)^2
=[(x-y+2z)-(x-2y-3z)][(x-y+2z)+(x-2y-3z)]
=(x-y+2z-x+2y+3z)(x-y+2z+x-2y-3z)
=(x-x+2y-y+2z+3z)(x+x-y-2y+2z-3z)
=(y+5z)(2x-3y-z)