3x(x-y)^3-6y(y-x)^2的值

题目

3x(x-y)^3-6y(y-x)^2的值

答案

因式分解得：
3x(x-y)^3-6y(y-x)^2
=3x(x-y)^3-6y(x-y)^2
=(x-y)²[3x(x-y)-6y]
=3(x-y)²(x²-xy-2y)
如果是化简,还要去括号：
3(x-y)²(x²-xy-2y)
=3(x²-2xy+y²)(x²-xy-2y)
=3(x^4-x^3y-2x²y-2x^3y+2x²y²+4xy²+x²y²-xy^3-2y^3)
=3(x^4-3x^3y-2x²y+3x²y²+4xy²-xy^3-2y^3)
=3x^4-9x^3y-6x²y+9x²y²+12xy²-3xy^3-6y^3