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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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