If $a = 3 + b$ , then what is the value of $a^{3} - b^{3} - 9 a b$

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Solution

Given,
$a = 3 + b$
or, $a - b = 3$ ....(1).
Now cubing both sides we get,
$a^{3} - b^{3} - 3 a b (a - b) = 27$
or, $a^{3} - b^{3} - 9 a b = 27$ . [ Using (1)]

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