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

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Solution

Given:- $a - b = 6 a b = 8$
To find:- $a^{3} - b^{3} = ?$
Sol:-
${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
${(6)}^{3} = a^{3} - b^{3} - 3 \cdot 8 \cdot (6)$
$\Rightarrow a^{3} - b^{3} = 216 + 144 = 360$

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