Evaluate the following using suitable identities: $(- 2 a - 3 b)^{3}$

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Solution

${(- 2 a - 3 b)}^{3}$
$\Rightarrow$ $- {(- 2 a + 3 b)}^{3}$ ( $∵$ ${(a + b)}^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2})$
$\Rightarrow$ $- [{(2 a)}^{3} + {(3 b)}^{3} + 3 \times {(2 a)}^{2} \times 3 b + 3 \times 2 a \times {(3 b)}^{2}]$
$\Rightarrow$ $- [3 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}]$

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