Question

因式分解（2x-y）^3-(x-2y)^3-(x+y)^3

因式分解

Answer 1

（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)

不懂的还可以问！满意请及时采纳！ O(∩_∩)O

Answer 2

(2x-y)³-(x-2y)³-(x+y)³
=(2x-y)³-[(x-2y)³+(x+y)³]
=(2x-y)³-[(x-2y)+(x+y)][(x-2y)²-(x-2y)(x+y)+(x+y)²]
=(2x-y)³-(2x-y)(x²-4xy+4y²-x²-xy+2xy+2y²+x²+2xy+y²)
=(2x-y)³-(2x-y)(x²-xy+7y²)
=(2x-y)[(2x-y)²-(x²-xy+7y²)]
=(2x-y)(4x²-4xy+y²-x²+xy-7y²)
=(2x-y)(3x²-3xy-6y²)
=3(2x-y)(x²-xy-2y²)
=3(2x-y)(x+2y)(x-y)