Question

分解因式 x^3-6(x^2)y+9 xy^2-4y^3

Answer 1

x³-6x²y+9 xy²-4y³

=x³-6x²y+5xy²+4xy²-4y³

=x(x²-6xy+5y²)+4y²(x-y)

=x(x-y)(x-5y)+4y²(x-y)

=(x-y)[x(x-5y)+4y²]

=(x-y)(x²-5xy+4y²)

=(x-y)(x-y)(x-4y)

=(x-y)²(x-4y)