Question:
Find the value
$125 x^{3}-27 y^{3}-225 x^{2} y+135 x y^{2}$
Solution:
$=(5 x)^{3}-(3 y)^{3}-3(5 x)^{2}(3 y)+3(5 x)(3 y)^{2}$
$\left[\therefore a^{3}-b^{3}-3 a^{2} b+3 a b^{2}=(a-b)^{3}\right]$
$=(5 x-3 y)^{3}$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
$\therefore 125 x^{3}-27 y^{3}-225 x^{2} y+135 x y^{2}$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
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