Find the value

Question:

Find the value

$8 a^{3}-b^{3}-4 a x+2 b x$

Solution:

$=(2 a)^{3}-b^{3}-2 x(2 a-b)$

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

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

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

$\therefore 8 a^{3}-b^{3}-4 a x+2 b x=(2 a-b)\left(4 a^{2}+2 a b+b^{2}-2 x\right)$

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