Factorize each of the following expressions:$x^3y^3+ 1$

Given:

$x^3y^3+ 1$

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,

$x^3y^3 + 1 = (xy)^3 + (1)^3$

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

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

Hence, $x^3y^3 + 1 = (xy + 1) (x^2y^2 - xy + 1)$.

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Updated on: 10-Oct-2022

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