Question:
Find the value
$x^{3} y^{3}+1$
Solution:
$=(x y)^{3}+1^{3}$
$=(x y+1)\left((x y)^{2}+x y+1^{2}\right)$
$\left[\therefore x^{3}+y^{3}=(x+y)\left(x^{2}-x y+y^{2}\right)\right]$
$=(x y+1)\left(x^{2} y^{2}-x y+1\right)$
$\therefore x^{3} y^{3}+1=(x y+1)\left(x^{2} y^{2}-x y+1\right)$
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