因式分解 ①2x(x+y)²-x(x+y)³
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因式分解 ①2x(x+y)²-x(x+y)³
因式分解 ①2x(x+y)²-x(x+y)³
②m(m-n)²-n(n-m)²
③2(x-y)²-x(x-y)
④m(a-b)-n(b-a)
因式分解 ①2x(x+y)²-x(x+y)³
②m(m-n)²-n(n-m)²
③2(x-y)²-x(x-y)
④m(a-b)-n(b-a)
![因式分解 ①2x(x+y)²-x(x+y)³](/uploads/image/z/18690224-32-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3+%E2%91%A02x%28x%2By%29%26%23178%3B-x%28x%2By%29%26%23179%3B)
①2x(x+y)²-x(x+y)³
=x(x+y)²[2-(x+y)]
=x(x+y)²(2-x-y)
②m(m-n)²-n(n-m)²
=m(m-n)²-n(m-n)²
=(m-n)²(m-n)
=(m-n)³
③2(x-y)²-x(x-y)
=(x-y)[2(x-y)-x]
=(x-y)(2x-2y-x)
=(x-y)(x-2y)
④m(a-b)-n(b-a)
=m(a-b)+n(a-b)
=(a-b)(m+n)
=x(x+y)²[2-(x+y)]
=x(x+y)²(2-x-y)
②m(m-n)²-n(n-m)²
=m(m-n)²-n(m-n)²
=(m-n)²(m-n)
=(m-n)³
③2(x-y)²-x(x-y)
=(x-y)[2(x-y)-x]
=(x-y)(2x-2y-x)
=(x-y)(x-2y)
④m(a-b)-n(b-a)
=m(a-b)+n(a-b)
=(a-b)(m+n)