Question

If $a-b=2$ and $\text{ab}=15$ then find the value of $a^3-b^3$.

Answer 1

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$\therefore a^3-b^3=(a-b)\left(\right(a-b{)}^2+3ab)$

$\therefore a^3-b^3=\left(2\right)(2^2+3(15\left)\right)$

$\therefore a^3-b^3=\left(2\right)(4+45)$

$\therefore a^3-b^3=\left(2\right)\left(49\right)$

$\therefore a^3-b^3=98$