将X⁴Y+X³Y²-X²Y²-XY⁴因式分解

将X⁴Y+X³Y²-X²Y²-XY⁴因式分解
将X⁴Y+X³Y²-X²Y²-XY⁴因式分解

将X⁴Y+X³Y²-X²Y²-XY⁴因式分解
X⁴Y+X³Y²-X²Y³-XY⁴ (这里可能是Y³)
=xy(x³+x²y-xy²-y³)
=xy[x²(x+y)-y²(x+y)]
=xy(x+y)(x²-y²)
=xy(x+y)²(x-y)

我觉得第三项应该是X^2Y^3吧

X²Y²应是X²Y3吧，原式=XY（X^3+X^2Y-XY^2-Y^3)=XY{[X^2(X+Y)-Y^2(X+Y)]}=XY(X+Y)(X^2-Y^2)
=XY(X-Y)(X+Y)^2