Question

Evaluate each expression if $\mathbf{a}\mathbf{=}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{b}\mathbf{=}\frac{\mathbf{2}}{\mathbf{3}}\mathbf{,}\mathbf{c}\mathbf{=}\mathbf{8}\mathbf{,}$ and $\mathbf{d}\mathbf{=}\mathbf{-}\mathbf{6}$.

9. $\mathbf{2}\mathbf{b}\left(\mathbf{4}\mathbf{a}\mathbf{+}{\mathbf{a}}^2\right)$$\mathbf{2}\mathbf{b}\left(\mathbf{4}\mathbf{a}\mathbf{+}{\mathbf{a}}^{\mathbf{2}}\right)$

Short answer

The valueof $2b\left(4a+a^2\right)$ is 60.

Step-by-step solution

– Description of step.

Substitute $-9$ for a into $a^2$.

${\left(-9\right)}^2=81$

– Description of step.

Substitute 81 for $a^2$, $-9$for a and $\frac{2}{3}$for b.

$2·\frac{2}{3}\left(4·\left(-9\right)+81\right)$

– Description of step.

Simplify the obtained equation in step 2.

$\begin{array}{c}\frac{4}{3}\left(-36+81\right)=\frac{4}{3}\cdot \left(45\right)\\ =60\end{array}$

Therefore, the value of $2b\left(4a+a^2\right)$ is 60.