Factorize the following expressions: x^4y^4 - xy - Vidyadip

Question

Factorize the following expressions:$ x^4y^4 - xy$

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Answer

$x^4 y^4-x y=x y\left(x^3 y^3-1\right)=x y\left((x y)^3-1^3\right)$
$=x y(x y-1)\left((x y)^2+x y \times 1+12\right)$
${\left[\therefore x^3-y^3=(x-y)\left(x^2+x y+y^2\right)\right]}$
$=x y(x y-1)\left(x^2 y^2+x y+1\right)$
$\therefore x^4 y^4-x y=x y(x y-1)\left(x^2 y^2+x y+1\right)$

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