Question

Factorize each of the following expression:
xy⁹ − yx⁹

Answer 1

$$\begin{gathered} x{y}^9-y{x}^9 \\ =xy(y^8-x^8) \\ =xy\left[\right(y^4{)}^2-\left(x^4{)}^2\right] \\ =xy(y^4+x^4)(y^4-x^4) \\ =xy(y^4+x^4)\left[\right(y^2{)}^2-\left(x^2{)}^2\right] \\ =xy(y^4+x^4)(y^2+x^2)(y^2-x^2) \\ =xy(y^4+x^4)(y^2+x^2)(y+x)(y-x) \end{gathered}$$