Question

若长方形的周长为28，两边长为x、y，且满足x³+x²y-xy²-y³=0。试求这个长方形的面积.

Answer 1

x³+x²y-xy²-y³=0
(x+y)²(x-y)=0
又x+y>0
故x-y=0
即x=y
又2(x+y)=28
4x=28
x=7
y=7

面积=7*7=49

追问

x³+x²y-xy²-y³=0得出(x+y)²(x-y)=0的过程？

追答

x³+x²y-xy²-y³=0
x²(x+y)-(x+y)y²=0
(x+y)(x²-y²)=0
(x+y)(x+y)(x-y)=0
(x+y)²(x-y)=0