Simplify :
$(4 x + 2 y)^{3} + (4 x - 2 y)^{3}$

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Solution

$(a + b)^{3} + (a - b)^{3} = [a^{3} + b^{3} + 3 a b (a + b)] + [a^{3} - b^{3} - 3 a b (a - b)]$
$= 2 (a^{3} + 3 a b^{2})$
Therefore,
$(4 x + 2 y)^{3} + (4 x - 2 y)^{3} = 2 [(4 x)^{3} + 3 \times 4 x \times (2 y)^{2}]$
$= 2 (64 x^{3} + 48 x y^{2})$
$= 128 x^{3} + 96 x y^{2}$

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