Question

In the following exercises, add or subtract the monomials.

$\begin{array}{l}\left(a\right)-12w+18w\\ \left(b\right)7x^{2}y-\left(-12x^{2}y\right)\end{array}$

Short answer

The result is

$\begin{array}{l}a)6w\\ b)19x^{2}y\end{array}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenexpressionsare}\\ \left(a\right)-12w+18w\\ \left(b\right)7x^{2}y-\left(-12x^{2}y\right)\\ \text{Wehavetoaddorsubtractthegivenexpressionsasapplicable.}\end{array}$

Step 2. Solving part (a)

$\begin{array}{l}\text{Considerthegivenexpression}\\ \Rightarrow -12w+18w=\left(-12+18\right)w\\ =6w\end{array}$

Step 2. Solving part (a)

$\begin{array}{l}\text{Considerthegivenexpression}\\ \Rightarrow 7x^{2}y-\left(-12x^{2}y\right)=7x^{2}y+12x^{2}y\\ =\left(7+12\right)x^{2}y\\ =19x^{2}y\end{array}$