求(x+y)^-4xy(x+y)的因式分解

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求(x+y)^-4xy(x+y)的因式分解
求(x+y)^-4xy(x+y)的因式分解

求(x+y)^-4xy(x+y)的因式分解
(x+y)^3-4xy(x+y)
=(x+y)[(x+y)^2-4xy]
=(x+y)(x^2+2xy+y^2-4xy)
=(x+y)(x^2-2xy+y^2)
=(x+y)(x-y)^2

(x+y)^2-4xy(x+y)
=(x+y)[(x+y)-4xy]
=(x+y)(x+y-4xy)

(x+y)³-4xy(x+y)
=(x+y)[(x+y)²-4xy]
=(x+y)(x-y)²

(x+y)^2-4xy(x+y)=(x+y)(x+y-4xy)