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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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