因式分解(2x-y)^3-(x-2y)^3-(x+y)^3

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

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

因式分解(2x-y)^3-(x-2y)^3-(x+y)^3
(2x-y)^3-(x-2y)^3-(x+y)^3
=[(2x-y)^3-(x-2y)^3]-(x+y)^3
=(2x-y-x+2y)[(2x-y)²+(2x-y)(x-2y)+(x-2y)²]-(x+y)^3
=(x+y)(7x²-13xy+7y²)-(x+y)³
=(x+y)[(7x²-13xy+7y²)-(x+y)²]
=(x+y)(6x²-15xy+6y²)
=3(x+y)(2x²-5xy+2y²)
=3(x+y)(x-2y)(2x-y)