因式分解2x^2y-x^3-xy^2 4-12(x-y）+9（x-y）^2

题目

因式分解2x^2y-x^3-xy^2 4-12(x-y）+9（x-y）^2
2x^2y-x^3-xy^2
4-12(x-y）+9（x-y）^2

答案

2x^2y-x^3-xy^2
=-x(x²-2xy+y²)
=-x(x-y)²
4-12(x-y）+9（x-y）^2
=[3(x-y)]²-2×2×[3(x-y)]+2²
=[3(x-y)-2]²
=(3x-3y-2)²