Factorize:$x^4 + x^2y^2 + y^4$

Given :

$x^4 + x^2y^2 + y^4$

To do :

We have to factorize the given expression.

Solution :

$x^4 + x^2y^2 + y^4  = (x^2)^2 + x^2y2 + (y^2)^2 + x^2y^2 - x^2y^2$           (Adding and subtracting $x^2y^2$)

$=(x^2)^2 + 2x^2y2 + (y^2)^2 - x^2y^2$

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

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

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

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

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Updated on: 10-Oct-2022

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