Q. 21 - Intermediate Algebra

Question

In the following exercises, add or subtract the monomials. 

$\begin{array}{l}\left(a\right)2a^2+b^2-6a^2\\ \left(b\right)x^{2}y-3x+7x{y}^2\end{array}$

Step-by-Step Solution

Answer

The required result is

$\begin{array}{l}a)-4a^2+6b^2\\ b)x^{2}y-3x+7x{y}^2\end{array}$

Step 1. Given information

$\begin{array}{l}\text{The given expression is}\\ \left(a\right)2a^2+b^2-6a^2\\ \left(b\right)x^{2}y-3x+7x{y}^2\\ \text{We have to add or subtract as applicable.}\end{array}$

Step 2. Solving part (a)

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

Step 3. Solving part (b)

$\begin{array}{l}\text{Consider the given expression}\\ \Rightarrow x^{2}y-3x+7x{y}^2\\ \left[\text{There are no like terms}\right]\\ \text{Thus,}\\ \text{After adding or subtracting the expression will remain the same}\end{array}$