Factorize:

Question:

Factorize:

$125-8 x^{3}-27 y^{3}-90 x y$

 

Solution:

$125-8 x^{3}-27 y^{3}-90 x y=5^{3}+(-2 x)^{3}+(-3 y)^{3}-3 \times 5 \times(-2 x) \times(-3 y)$

$=[5+(-2 x)+(-3 y)]\left[5^{2}+(-2 x)^{2}+(-3 y)^{2}-5 \times(-2 x)-(-2 x)(-3 y)-5 \times(-3 y)\right]$

$=(5-2 x-3 y)\left(25+4 x^{2}+9 y^{2}+10 x-6 x y+15 y\right)$

 

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