Without actually calculating cubes, value of each of following : (-12)^{3}+(7)^{3}+(5)^{3}

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2. Polynomials

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Without actually calculating the cubes, find the value of each of the following : $(-12)^{3}+(7)^{3}+(5)^{3}$

A

$1165$

B

$-1165$

C

$-1260$

D

$1260$

Solution

Let $x=-12, y=7$ and $z=5$

Then $x+y+z=-12+7+5=0$

We know that if $x+y+z=0,$ then $x^{3}+y^{3}+z^{3}=3 x y z$

$\therefore $ $ (-12)^{3}+(7)^{3}+(5)^{3} =3[(-12)(7)(5)] $ $[\because(-12)+7+5=0]$

$ =3[-420]=-1260 $

Thus, $ (-12)^{3}+(7)^{3}+(5)^{3} =-1260$

Standard 9

Mathematics

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