Question:
Find the value
$54 x^{6} y+2 x^{3} y^{4}$
Solution:
$=2 x^{3} y\left(27 x^{3}+y^{3}\right)$
$=2 x^{3} y\left((3 x)^{3}+y^{3}\right)$
$=2 x^{3} y(3 x+y)\left((3 x)^{2}-3 x x y+y^{2}\right)$
$\therefore\left[a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right]$
$=2 x^{3} y(3 x+y)\left(9 x^{2}-3 x y+y^{2}\right)$
$\therefore 54 x^{6} y+2 x^{3} y^{4}=2 x^{3} y(3 x+y)\left(9 x^{2}-3 x y+y^{2}\right)$
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