Question

Factorize:
$x{y}^9-y{x}^9$

Answer 1

Given: $x{y}^9-y{x}^9$
$\therefore x{y}^9-y{x}^9$
$=xy(y^8-x^8)$
$=xy\left[\right(y^4{)}^2-\left(x^4{)}^2\right]$
$=xy\left[\right(y^4+x^4\left)\right(y^4-x^4\left)\right]$
$=xy(y^4+x^4)(y^2+x^2)(y^2-x^2)$
$=xy(y^4+x^4)(y^2+x^2)(y+x)(y-x)$

Hence, $x{y}^9-y{x}^9$
$=xy(y^4+x^4)(y^2+x^2)(y+x)(y-x)$