Q. 22 - Intermediate Algebra

Question

In the following exercises, add or subtract the monomials. 

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

Step-by-Step Solution

Answer

The required result is

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

Step 1. Given information

$\begin{array}{l}\text{The given expression is}\\ \left(a\right)5u^2+4v^2-6u^2\\ \left(b\right)12a+8b\\ \text{We have to add or subtract as applicable.}\end{array}$

Step 2. Solving part (a)

$\begin{array}{l}\text{Consider the given expression}\\ \Rightarrow 5u^2+4v^2-6u^2=5u^2-6u^2+4v^2\left[\text{Combine the like terms}\right]\\ =\left(5-6\right)u^2+4v^2\\ =-u^2+4v^2\end{array}$

Step 3. Solving for part (b)

$\begin{array}{l}\text{Consider the given expression}\\ \Rightarrow 12a+8b\\ \left[\text{There are no like terms}\right]\\ \text{Thus,}\\ \text{After adding or subtracting the expression will remain the same}\end{array}$