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

Given:

$x^4y^4 - xy$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

$x^4y^4 - xy = xy(x^3y^3 - 1)$

$= xy[(xy)^3-(1)^3]$

$= xy (xy - 1) [(xy)^2 + xy \times 1 + 1^2]$

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

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

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Updated on: 10-Oct-2022

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