(x-y)^4+x(x-y)^3-y(y-x)^3因式分解
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(x-y)^4+x(x-y)^3-y(y-x)^3因式分解
(x-y)^4+x(x-y)^3-y(y-x)^3
(x-y)^4+x(x-y)^3-y(y-x)^3
![(x-y)^4+x(x-y)^3-y(y-x)^3因式分解](/uploads/image/z/3310803-27-3.jpg?t=%28x-y%29%5E4%2Bx%28x-y%29%5E3-y%28y-x%29%5E3%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
原式=(x-y)^4+x(x-y)^3+y(x-y)^3
=(x-y)^4+(x+y)(x-y)^3
=(x-y)^3((x-y)+(x+y))
=2x(x-y)^3
再问: =(x-y)^4+(x+y)(x-y)^3怎么得出来的。。。
再答: x(x-y)^3+y(x-y)^3有公因式(x-y)^3,提公因式嘛
=(x-y)^4+(x+y)(x-y)^3
=(x-y)^3((x-y)+(x+y))
=2x(x-y)^3
再问: =(x-y)^4+(x+y)(x-y)^3怎么得出来的。。。
再答: x(x-y)^3+y(x-y)^3有公因式(x-y)^3,提公因式嘛