Question

Evaluate the following:

(ii) ${46}^3+{34}^3$

Answer 1

Given, ${46}^3+{34}^3$

Using Identity,

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

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

$\therefore {46}^3+{34}^3$

$=(46+34{)}^3-3\times 46\times 34(46+34)$

$=(80{)}^3-3\times 46\times 34(80)$

$=512000-4692\left(80\right)$

$=512000-375360$

$=136640$

$\therefore {46}^3+{34}^3=136640$