Question
Factories : $64 a^3-27 b^3-144 a^2 b+108 a b^2$
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Answer
$64 a^3-27 b^3-144 a^2 b+108 a b^2$
$=(4 a)^3-(3 b)^3-3(4 a)(3 b)(4 a-3 b)$
$=(4 a-3 b)^3$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=(4 a-3 b)(4 a-3 b)(4 a-3 b)$
$=(4 a)^3-(3 b)^3-3(4 a)(3 b)(4 a-3 b)$
$=(4 a-3 b)^3$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=(4 a-3 b)(4 a-3 b)(4 a-3 b)$
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