Question
Factorise:
$x^4 y^4-x y$
$x^4 y^4-x y$
✓
Answer
$x^4 y^4-x y$
$=x y\left(x^3 y^3-1\right)$
$=x y\left[(x y)^3-(1)^3\right]$
$=x y\left\{(x y-1)\left[(x y)^2+(x y)(1)+(1)^2\right]\right\}$
$=x y(x y-1)\left(x^2 y^2+x y+1\right)$
$=x y\left(x^3 y^3-1\right)$
$=x y\left[(x y)^3-(1)^3\right]$
$=x y\left\{(x y-1)\left[(x y)^2+(x y)(1)+(1)^2\right]\right\}$
$=x y(x y-1)\left(x^2 y^2+x y+1\right)$
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