Question

Evaluate the following:

(iv) ${93}^3-{107}^3$

Answer 1

Given, ${93}^3-{107}^3$

Using Identity,

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

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

$\therefore {93}^3-{107}^3$

$=(93-107{)}^3+3\times 93\times 107(93-107)$

$=(-14{)}^3+3\times 93\times 107(-14)$

$=-2744+29853(-14)$

$=-2744-417942$

$=-420686$

$\therefore {93}^3-{107}^3=-420686$