Question

phân tích đa thức sau thành phân tử x^3-3x^2y+3xy^2-y^3-z^3

Answer 1

\(x^3-3x^2y+3xy^2-y^3-z^3\)

\(=\left(x-y\right)^3-z^3\)

\(=\left(x-y-z\right)\left[\left(x-y\right)^2+z\left(x-y\right)+z^2\right]\)

Answer 2

\(x^3-3x^2y+3xy^2-y^3-z^3\\ =\left(x-y\right)^3-z^3\\ =\left(x-y-z\right)\left(x^2-2xy+y^2+zy-xz+z^2\right)\\ =\left(x-y-z\right)\left(x^2+y^2+z^2+2xy+zy-zx\right)\)