Q. 5.4 - Intermediate Algebra

Question

Add or subtract: $\text{ (a) }-15c^2+8c^2\text{ (b) }-15y^2{z}^3-\left(-5y^2{z}^3\right)$

Step-by-Step Solution

Answer

The result is

$\begin{array}{l}a)-7c^2\\ b)-10y^2{z}^3\end{array}$

Step 1. Given information

The given polynomials are

$$\begin{gathered} \text{ (a) }-15c^2+8c^2 \\ \text{(b) }-15y^2{z}^3-\left(-5y^2{z}^3\right) \end{gathered}$$

We have to add or subtract the terms as applicable

Step 2. Solve part (a)

$\begin{array}{l}\text{We have (a) }-15c^2+8c^2\text{. }\\ \text{Combine the like terms}\\ \Rightarrow -15c^2+8c^2=\left(-15+8\right)c^2\\ =7c^2\end{array}$

Step 3. Solve part (b)

$\begin{array}{l}\text{We have (b) }-15y^2{z}^3-\left(-5y^2{z}^3\right)\text{.}\\ \Rightarrow -15y^2{z}^3-\left(-5y^2{z}^3\right)=-15y^2{z}^3+5y^2{z}^3\\ \text{Combine the like terms}\\ =\left(-15+5\right)y^2{z}^3\\ =-10y^2{z}^3\end{array}$