Question

Factorize each of the following expressions:
$x^4{y}^4-xy$

Answer 1

Given:$x^4{y}^4-xy$

$\therefore x^4{y}^4-xy$
$=xy(x^3{y}^3-1)$
$=xy\left[\right(xy{)}^3-\left(1{)}^3\right]$
$=xy(xy-1)\left[\right(xy{)}^2+xy\times 1+\left(1{)}^2\right]$
$[\therefore a^3-b^3=(a-b\left)\right(a^2+ab+b^2\left)\right]$

$=xy(xy-1)(x^2{y}^2+xy+1)$

Hence,$x^4{y}^4-xy=xy(xy-1)(x^2{y}^2+xy+1).$