Question

Find the difference between the value of $5m^3-4m$ and $2m^2+9$, when $m=-2$ .

Answer 1

Given the two expressions as :

$5m^3-4m$ and $2m^2+9$

Step 1 Finding the value of the expression $\mathbf{5}{\mathit{m}}^{\mathbf{3}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{4}\mathit{m}$ at $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{}$:

At $m=-2$,

$$\begin{gathered} 5m^3-4m=5{\left(-2\right)}^3-4\left(-2\right) \\ =5\left(-8\right)+8 \\ =-40+8 \\ =-32 \end{gathered}$$

So, at $m=-2$

$5m^3-4m=-32$

Step 2 Finding the value of the expression $\mathbf{2}{\mathit{m}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{9}$ at $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{}$:

$$\begin{gathered} 2m^2+9=2{\left(-2\right)}^2+9 \\ =2\left(4\right)+9 \\ =8+9 \\ =17 \end{gathered}$$

So, at $m=-2$

$2m^2+9=17$

Step 3 Finding the difference between respective values of the expressions at $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{}$:

So at $m=-2$

$$\begin{gathered} \left(5m^3-4m\right)-\left(2m^2+9\right)=\left(-32\right)-\left(17\right) \\ =-32-17 \\ =-49 \end{gathered}$$

Therefore , at $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{}$

$\left(5m^3-4m\right)\mathbf{}\mathbf{-}\mathbf{}\left(2m^2+9\right)\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{49}$