6(x-2y)²(x+2y)-7(x-2y)(x+2y)+2(x+2y)³﹙m-n﹚³-5n﹙n-m﹚²-6﹙n-m﹚n²分解因式
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![6(x-2y)²(x+2y)-7(x-2y)(x+2y)+2(x+2y)³﹙m-n﹚³-5n﹙n-m﹚²-6﹙n-m﹚n²分解因式](/uploads/image/z/3952669-13-9.jpg?t=6%28x-2y%29%26%23178%3B%28x%2B2y%29-7%EF%BC%88x-2y%EF%BC%89%EF%BC%88x%2B2y%EF%BC%89%2B2%EF%BC%88x%2B2y%EF%BC%89%26%23179%3B%EF%B9%99m-n%EF%B9%9A%26%23179%3B-5n%EF%B9%99n-m%EF%B9%9A%26%23178%3B-6%EF%B9%99n-m%EF%B9%9An%26%23178%3B%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F)
6(x-2y)²(x+2y)-7(x-2y)(x+2y)+2(x+2y)³﹙m-n﹚³-5n﹙n-m﹚²-6﹙n-m﹚n²分解因式
6(x-2y)²(x+2y)-7(x-2y)(x+2y)+2(x+2y)³
﹙m-n﹚³-5n﹙n-m﹚²-6﹙n-m﹚n²
分解因式
6(x-2y)²(x+2y)-7(x-2y)(x+2y)+2(x+2y)³﹙m-n﹚³-5n﹙n-m﹚²-6﹙n-m﹚n²分解因式
1.设u=x-2y,v=x+2y,则原式=6u^2v-7uv+2v^3,非齐次,无法分解,
若改为原式=6u^2v-7uv^2+2v^3,则
原式=v(6u^2-7uv+2v^2)=v(3u-2v)(2u-v)
=(x+2y)[3(x-2y)-2(x+2y)][2(x-2y)-(x+2y)]
=(x+2y)(x-10y)(x-6y).
2.设x=m-n,则原式=x^3-5nx^2+6xn^2=x(x^2-5nx+6n^2)=x(x-2n)(x-3n)
=(m-n)(m-3n)(m-4n).