Question

If a - b = 6 and ab = 20, find the value of $a^3-b^3$.

Answer 1

a - b = 6, ab = 20

Cubing both sides,

$(a-b{)}^3=(6{)}^3\Rightarrow a^3-b^3-3ab(a-b)=216\Rightarrow a^3-b^3-3\times 20\times 6=216\Rightarrow a^3-b^3-360=216\Rightarrow a^3-b^3=216+360=576\therefore a^3-b^3=576$