Question:
Find the value
$8 a^{3}-27 b^{3}-36 a^{2} b+54 a b^{2}$
Solution:
$=(2 a)^{3}-(3 b)^{3}-3 \times(2 a)^{2} \times 3 b+3 \times 2 a \times(3 b)^{2}$
$=(2 a-3 b)^{3}$
$\left[\therefore a^{3}-b^{3}-3 a^{2} b+3 a b^{2}=(a-b)^{3}\right]$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
$\therefore 8 a^{3}-27 b^{3}-36 a^{2} b+54 a b^{2}$
$=(2 a-3 b)(2 a-3 b)(2 a-3 b)$
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