Factorise:
$6 (x + 2 y)^{3} + 8 (x + 2 y)^{2}$

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Solution

Given $6 (x + 2 y)^{3} + 8 (x + 2 y)^{2}$
$= (x + 2 y)^{2} {6 (x + 2 y) + 8}$
$= (x + 2 y)^{2} {(6 x + 12 y + 8)}$
$= (x + 2 y)^{2} (6 x + 12 y + 8)$ .
$= 2 (3 x + 6 y + 4) (x + 2 y)^{2}$
Therefore, the factors of the given expression is
$2 (3 x + 6 y + 4) (x + 2 y)^{2}$

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