Question

Add or subtract:$\text{(a)}12q^2+9q^2\text{(b)}8m{n}^3-\left(-5m{n}^3\right)\text{.}$

Short answer

The result is

$\begin{array}{l}a)21q^2\\ b)13m{n}^3\end{array}$

Step-by-step solution

Step 1. Given information

The given polynomials are

$$\begin{gathered} \text{(a)}12q^2+9q^2 \\ \text{(b)}8m{n}^3-\left(-5m{n}^3\right)\text{.} \end{gathered}$$

We have to add or subtract the terms as applicable

Step 2. Solve part (a)

$\begin{array}{l}\text{Wehave(a)}12q^2+9q^2\\ \text{Combinetheliketerms}\\ \Rightarrow 12q^2+9q^2=\left(12+9\right)q^2\\ =21q^2\end{array}$

Step 3. Solve part (b)

$\begin{array}{l}\text{Wehave(b)}8m{n}^3-\left(-5m{n}^3\right)\text{.}\\ \text{Combinetheliketerms}\\ \Rightarrow 8m{n}^3-\left(-5m{n}^3\right)=\left(8+5\right)m{n}^3\\ =13m{n}^3\end{array}$