If $a + b = 6$ and $a b = 8$ , find $a^{3} + b^{3}$ .

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Solution

By using formula, ${(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)$
Substituting $a + b = 6; a b = 8$ ,
$6^{3} = a^{3} + b^{3} + 3 \times 8 \times 6$
$216 = a^{3} + b^{3} + 144$
$a^{3} + b^{3} = 216 - 144 = 72$

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