Question

Simplify $a(a^2+a+1)+5$ and find its value for a = 1.

Answer 1

Consider

$\begin{array}{l}\mathbf{a}\left({\mathbf{a}}^2+\mathbf{a}+\mathbf{1}\right)+\mathbf{5}\\ ={\mathbf{a}}^3+{\mathbf{a}}^2+\mathbf{a}+\mathbf{5}\\ \text{At}\mathbf{a}=\mathbf{1}\\ ={\mathbf{1}}^3+{\mathbf{1}}^2+\mathbf{1}+\mathbf{5}\\ =\mathbf{1}+\mathbf{1}+\mathbf{1}+\mathbf{5}\\ =\mathbf{8}\end{array}$

Hence simplified.