把下列各式分解因式 (x+y)^2-(2x-y)^2 9(2x-y)^2-4(x+2y)^2 (m-1)^2-64 (am+bm+c)^2-(am+bm-c)^2

题目

把下列各式分解因式 (x+y)^2-(2x-y)^2 9(2x-y)^2-4(x+2y)^2 (m-1)^2-64 (am+bm+c)^2-(am+bm-c)^2

答案

(x+y)^2-(2x-y)^2=（x+y+2x-y）（x+y-2x+y）=3x(2y-x)9(2x-y)^2-4(x+2y)^2 =[3(2x-y)+2(x+2y)][3(2x-y)-2(x+2y)]=(8x+y)(4x-7y)(m-1)^2-64=(m-1+8)(m-1-8)=(m+7)(m-9)(am+bm+c)^2-(am+bm-c)^2=(am+bm+c+am+bm-c)(am+...