Question

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

Short answer

The result is

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

Step-by-step solution

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) 

$\begin{array}{l}\text{Wehave(a)}-15c^2+8c^2\text{.}\\ \text{Combinetheliketerms}\\ \Rightarrow -15c^2+8c^2=\left(-15+8\right)c^2\\ =7c^2\end{array}$

Step 3. Solve part (b) 

$\begin{array}{l}\text{Wehave(b)}-15y^2{z}^3-\left(-5y^2{z}^3\right)\text{.}\\ \Rightarrow -15y^2{z}^3-\left(-5y^2{z}^3\right)=-15y^2{z}^3+5y^2{z}^3\\ \text{Combinetheliketerms}\\ =\left(-15+5\right)y^2{z}^3\\ =-10y^2{z}^3\end{array}$