If $a - b = 3 a n d a b = 10;$ find $a^{3} - b^{3}$

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Solution

$a - b = 3 \Rightarrow (a - b)^{3} = (3)^{3} \Rightarrow a^{3} - b^{3} - 3 a b (a - b) = 27 \Rightarrow a^{3} - b^{3} - 3 \times 10 (3) = 27 \Rightarrow a^{3} - b^{3} - 90 = 27 \Rightarrow a^{3} - b^{3} = 27 + 90 \Rightarrow a^{3} - b^{3} = 117$ .

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