Question
Factorize the following expressions: $x^3y^3 + 1$
✓
Answer
$x^3y^3 + 1 = (xy)^3 + 1^3 = (xy + 1)((xy)^2 + xy + 1^2)$
$\big[\therefore$ $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$
$\big]$ $= (xy + 1)(x^2y^2 - xy + 1)$
$\therefore$ $x^3y^3 + 1 = (xy + 1)(x^2y^2 - xy + 1)$
$\big[\therefore$ $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$
$\big]$ $= (xy + 1)(x^2y^2 - xy + 1)$
$\therefore$ $x^3y^3 + 1 = (xy + 1)(x^2y^2 - xy + 1)$
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