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

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Solution

$(2 x + y)^{3} + (2 x - y)^{3}$
$\Rightarrow$ $[(2 x)^{2}]^{3} - [(y)^{2}]^{3}$ [ Since, $(a + b) (a - b) = a^{2} - b^{2}]$
$\Rightarrow$ $[4 x^{2}]^{3} - [y^{2}]^{3}$
$\Rightarrow$ $64 x^{6} - y^{6}$
$∴$ $(2 x + y)^{3} + (2 x - y)^{3} = 64 x^{6} - y^{6}$

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