Question

In the following exercises, find the product of $\left(r^2\hspace{0.17em}-\hspace{0.17em}{s}^3\right)\left(r^3\hspace{0.17em}+\hspace{0.17em}{s}^2\right)$ .

Short answer

The product of $\left(r^2\hspace{0.17em}-\hspace{0.17em}{s}^3\right)\left(r^3\hspace{0.17em}+\hspace{0.17em}{s}^2\right)$is $r^5+r^2{s}^2-s^3{r}^3-s^5$.

Step-by-step solution

Step 1. Given Information.

The given expression is $\left(r^2\hspace{0.17em}-\hspace{0.17em}{s}^3\right)\left(r^3\hspace{0.17em}+\hspace{0.17em}{s}^2\right)$.

Step 2. Solve for the multiplication of given expression.

Multiply the expression $\left(r^2\hspace{0.17em}-\hspace{0.17em}{s}^3\right)\left(r^3\hspace{0.17em}+\hspace{0.17em}{s}^2\right)$

$$\begin{gathered} \left(r^2\hspace{0.17em}-\hspace{0.17em}{s}^3\right)\left(r^3\hspace{0.17em}+\hspace{0.17em}{s}^2\right)=r^2{r}^3+r^2{s}^2-s^3{r}^3-s^3{s}^2 \\ {r}^2{r}^3+r^2{s}^2-s^3{r}^3-s^3{s}^2=r^5+r^2{s}^2-s^3{r}^3-s^5 \end{gathered}$$