Question

Without actually calculating the cubes find the value of (1by2)whole cube+(1by3)whole cube-(5by6)whole cube

Answer 1

$- \frac{5}{12}$

EXPLAINATION

$( \frac{1}{2}) {}^{3} + ( \frac{1}{3} ){}^{3} - (\frac{5}{6}) {}^{3}$

${( \frac{1}{2} + \frac{1}{3}) }^{3} - 3.\frac{1}{2}. \frac{1}{3}( \frac{1}{2} + \frac{1}{3} ) - {( \frac{5}{6} )}^{3}$

${( \frac{5}{6} )}^{3} - \frac{1}{2} \frac{5}{6} - {( \frac{5}{6}) }^{?}$

$- \frac{5}{12}$