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