Factorize:
Question:

Factorize:

$2 a^{3}+16 b^{3}-5 a-10 b$

 

Solution:

$2 a^{3}+16 b^{3}-5 a-10 b=2\left[a^{3}+8 b^{3}\right]-5(a+2 b)$

$=2\left[a^{3}+(2 b)^{3}\right]-5(a+2 b)$

$=2(a+2 b)\left[a^{2}-a \times 2 b+(2 b)^{2}\right]-5(a+2 b)$

$=2(a+2 b)\left(a^{2}-2 a b+4 b^{2}\right)-5(a+2 b)$

$=(a+2 b)\left[2\left(a^{2}-2 a b+4 b^{2}\right)-5\right]$

 

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