Question:
Factorise
$64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$
Solution:
$64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}=(4 a)^{3}-(3 b)^{3}-3(4 a)^{2}(3 b)+3(4 a)(3 b)^{2}$
$=(4 a-3 b)^{3}$
Hence, factorisation of $64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$ is $(4 a-3 b)^{3}$.
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