without finding cubes, find value of (1/4)³+(1/3)³-(7/12)3 please explain in DETAIL

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Question

without finding cubes, find value of
(1/4)3+(1/3)3-(7/12)3 please explain in
DETAIL

Aakash Sharma · Accepted Answer

Since

$\frac{1}{4} + \frac{1}{3} + (- \frac{7}{12}) = \frac{3 + 4}{4 \times 3} - \frac{7}{12} = \frac{7 - 7}{12} = 0$

Thus

${(\frac{1}{4})}^{3} + {(\frac{1}{3})}^{3} + {(- \frac{7}{12})}^{3} = 3 \times \frac{1}{4} \times \frac{1}{3} \times (- \frac{7}{12}) = - \frac{7}{48}$

without finding cubes, find value of (1/4)3+(1/3)3-(7/12)3 please explain in DETAIL

without finding cubes, find value of (1/4)³+(1/3)³-(7/12)3 please explain in DETAIL