Find the value

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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