x3+y3+3x2y-5xy2因式分解
问题描述：
x3+y3+3x2y-5xy2因式分解
答
=x³+y³+3x²y-5xy²
=x³-x²y+4x²y-4xy²-xy²+y³
=x²(x-y)+4xy(x-y)-y²(x-y)
=(x-y)(x²+4xy-y²)在实数范围内=x³+y³+3x²y-5xy²=x³-x²y+4x²y-4xy²-xy²+y³=x²(x-y)+4xy(x-y)-y²(x-y)=(x-y)(x²+4xy-y²)=(x-y)(x²+4xy+4y²-5y²)=(x-y)[(x²+4xy+4y²)-5y²]=(x-y)[(x+2y)²-5y²]=(x-y)(x+2y+√5y)(x+2y-√5y)