Question

求解x²(x+1)-y(xy+x)

是分解因式

Answer 1

x²(x+1)-y(xy+x)
=x³+x²-xy²-xy
=(x³-xy²)+(x²-xy).......分组
=x(x²-y²)+x(x-y)........提取公因式
=x(x+y)(x-y)+x(x-y).....平方差公式
=x(x-y)[(x+y)+1]......提取公因式
=x(x-y)(x+y+1)

Answer 2

原式=x²(x+1)-y²(x+1)
=(x+1)(x²-y²)
(x+1)(x+y)(x-y)