Question

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 (a

Answer 1

(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+bm+c-am-bm+c)

=2(am+bm)*2c

=4mc(a+b)

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