Factorise : 8 a^3-b^3-12 a^2 b+6 a b^2 - Vidyadip

Question

Factorise : $8 a^3-b^3-12 a^2 b+6 a b^2$

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Answer

$8 a^3-b^3-12 a^2 b+6 a b^2$
$=(2 a)^3-(b)^3+3(2 a)(b)(2 a-b)$
$=(2 a-b)^3$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=(2 a-b)(2 a-b)(2 a-b)$

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