Factorise
Question:

Factorise

$27 a^{3}+64 b^{3}$

 

Solution:

We know that 

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

Given: $27 a^{3}+64 b^{3}$

$x=3 a, y=4 b$

$27 a^{3}+64 b^{3}=(3 a+4 b)\left(9 a^{2}+16 b^{2}-12 a b\right)$

 

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