因式分解3xy²-6xy²+9y³

题目

因式分解3xy²-6xy²+9y³
是3x²y-6xy²+9y³

答案

3x²y-6xy²+9y³
=3y(x²-2xy+y²+2y²)
=3y［(x-y)²+2y²］
=3y［(x-y)²-(-2)y²］
=3y［x-y-√(-2)y］［x-y+√(-2)y］