因式分解(2x+y)^2-(x+2y)^2

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因式分解(2x+y)^2-(x+2y)^2
因式分解(2x+y)^2-(x+2y)^2

因式分解(2x+y)^2-(x+2y)^2
(2x+y)^2-(x+2y)^2
=(2x+y-x-2y)(2x+y+x+2y)
=(x-y)(3x+3y)
=3(x-y)(x+y)

3（x^2-y^2）

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

(2x+y)^2-(x+2y)^2
=4x^2+y^2+4xy-x^2-4y^2-4xy
=3x^2-3y^2
=3(x+y)(x-y)

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