Question

Without actually the cubes, find the value of each of the following
$\left(i\right){\left(-12\right)}^3+{\left(7\right)}^3+{\left(5\right)}^3$
$\left(ii\right){\left(28\right)}^3+{\left(-15\right)}^3+{\left(-13\right)}^3$

Answer 1

Part (1)

Given that,

${(-12)}^3+{\left(7\right)}^3+{\left(5\right)}^3$
We know that,

$(a+b+c)=0,a^3+b^3+c^3=3abc$
Here $a=-12,b=7andc=5$
Hence ${(-12)}^3+{\left(7\right)}^3+{\left(5\right)}^3=3\times (-12)\times 7\times 5=-1260$

Part (2)

Given ${\left(28\right)}^3+{(-15)}^3+{(-13)}^3$
We know that, $(a+b+c)=0,a^3+b^3+c^3=3abc$
Here $a=28,b=-15andc=-13$

Hence ${\left(28\right)}^3+{(-15)}^3+{(-13)}^3=3\times 28\times (-15)\times (-13)=16380$