Question

If $a=4$ , $b=0$ and $c=-1$ , find the value of the following :

$a^3+b^3+c^3-3abc$

Answer 1

Given that $a=4$ , $b=0$ and $c=-1$ ,

We have to find the value of the expression :

$a^3+b^3+c^3-3abc$

Finding the value of the expression at the given value of variables :

At $a=4$ , $b=0$ and $c=-1$ ,

$$\begin{gathered} a^3+b^3+c^3-3abc={\left(4\right)}^3+{\left(0\right)}^3+{\left(-1\right)}^3-3\left(4\right)\left(0\right)\left(-1\right) \\ =64+0+\left(-1\right)-0 \\ =64+0-1-0 \\ =64-1 \\ =63 \end{gathered}$$

Therefore , value of the given expression at $\mathit{a}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}$ , $\mathit{b}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$ and $\mathit{c}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{1}$ is :

${\mathit{a}}^{\mathbf{3}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{b}}^{\mathbf{3}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{c}}^{\mathbf{3}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{3}\mathit{a}\mathit{b}\mathit{c}\mathbf{}\mathbf{=}\mathbf{}\mathbf{63}$