Question

If $a-b=5,$ and $ab=14$ find the value of $a^3-b^3$.

Answer 1

From question,

$a-b=5$

and $ab=14$

We have ${(a-b)}^3=a^3-b^3-3ab(a-b)$

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

$={\left(5\right)}^3+3\times 14\left(5\right)$

$=125+210‬=335$

$\therefore a^3-b^3=335$