Question

In the following exercises, find the product of $\left(r^6\hspace{0.17em}+\hspace{0.17em}{s}^6\right)\left(r^6\hspace{0.17em}-\hspace{0.17em}{s}^6\right)$.

Short answer

The product of $(r^6+s^6)(r^6-s^6)$ is $r^{12}-s^{12}$.

Step-by-step solution

Step 1. Given Information

The given expression is $\left(r^6+s^6\right)\left(r^6-s^6\right)$.

Step 2. Solve for the multiplication of given expression.

Multiply the expression $\left(r^6+s^6\right)\left(r^6-s^6\right)$

$$\begin{gathered} \left(r^6+s^6\right)\left(r^6-s^6\right)={\left(r^6\right)}^2-{\left(s^6\right)}^2-s^6{r}^6+s^6{r}^6 \\ {\left(r^6\right)}^2-{\left(s^6\right)}^2=r^{12}-s^{12} \end{gathered}$$