因式分解 x³+x²y-xy²-y³ a²-b²+a+b 16-1/25m²

因式分解 x³+x²y-xy²-y³ a²-b²+a+b 16-1/25m²
因式分解 x³+x²y-xy²-y³ a²-b²+a+b 16-1/25m²

因式分解 x³+x²y-xy²-y³ a²-b²+a+b 16-1/25m²
解1: x³+x²y-xy²-y³
=x^3-y^3+x^2y-xy^2
=(x+y)(x^2-xy+y^2)+xy(x+y)
=(x+y)(x^2+y^2)
解2.a²-b²+a+b
=（a+b）(a-b)+a+b
=(a+b)(a-b+1)
解3.16-1/25m²
=（4+m/5）(4-m/5)

x³+x²y-xy²-y³=x²(x+y)-y²(x+y)=(x²-y²)(x+y)=[(x+y)(x-y)](x+y)=(x+y)²(x-y)
a²-b²+a+b=(a+b)(a-b)+(a+b)=(a+b)(a-b+1)
16-1/25m²=(16m²-1)/25m²=[(4m+1)(4m-1)]/25m²