Question

In the following exercises, add or subtract the monomials.

$$\begin{gathered} \left(a\right)5u^2+4v^2-6u^2 \\ \left(b\right)12a+8b \end{gathered}$$

Short answer

The required result is

$\begin{array}{l}a)-u^2+4v^2\\ b)12a+8b\end{array}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionis}\\ \left(a\right)5u^2+4v^2-6u^2\\ \left(b\right)12a+8b\\ \text{Wehavetoaddorsubtractasapplicable.}\end{array}$

Step 2. Solving part (a)

$\begin{array}{l}\text{Considerthegivenexpression}\\ \Rightarrow 5u^2+4v^2-6u^2=5u^2-6u^2+4v^2\left[\text{Combinetheliketerms}\right]\\ =\left(5-6\right)u^2+4v^2\\ =-u^2+4v^2\end{array}$

Step 3. Solving for part (b)

$\begin{array}{l}\text{Considerthegivenexpression}\\ \Rightarrow 12a+8b\\ \left[\text{Therearenoliketerms}\right]\\ \text{Thus,}\\ \text{Afteraddingorsubtractingtheexpressionwillremainthesame}\end{array}$