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

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Solution

by using formula;- $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
We have,
$\begin{matrix} = (2 x - 3 - (2 x - 3)) ({(2 x + 3)}^{2} + (2 x + 3) (2 x - 3) + {(2 x - 3)}^{2}) = (2 x - 3 - 2 x + 3) (4 x + 9 + 12 x + 4 x^{2} - 6 x + 6 x - 9 + 4 x + 9 - 12 x) = 4 x^{2} + 8 x + 9 \end{matrix}$
on simplifying we get, $(4 x^{2} + 8 x + 9)$

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