Factorise: 8 a^3-b^3-4 a x+2 b x - Vidyadip

Question

Factorise:
$8 a^3-b^3-4 a x+2 b x$

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Answer

$8 a^3-b^3-4 a x+2 b x$
$=8 a^3-b^3-2 x(2 a-b)$
$=(2 a)^3-(b)^3-2 x(2 a-b) \text { Since } a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
$=(2 a-b)\left[(2 a)^2+2 a \times b+(b)^2\right]-2 x(2 a-b)$
$=(2 a-b)\left(4 a^2+2 a b+b^2\right)-2 x(2 a-b)$
$=(2 a-b)\left(4 a^2+2 a b+b^2-2 x\right)$

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