Q. 272 - Intermediate Algebra

Question

In the following exercises , simplify the equation $\left(rs\hspace{0.17em}-27\right)\left(rs\hspace{0.17em}+27\right)$ .

Step-by-Step Solution

Answer

The simplified expression is $r^2{s}^2-729$.

Step 1. Given Information.

The expression is $\left(rs\hspace{0.17em}-27\right)\left(rs\hspace{0.17em}+27\right)$ .

Step 2. Simplify given equation.

Simplifying $\left(rs\hspace{0.17em}-27\right)\left(rs\hspace{0.17em}+27\right)$

Apply Difference of two square formula , we get:-

$\begin{array}{rcl}\left(a-b\right)\left(a+b\right)& =& a^2-b^2\\ \left(rs-27\right)\left(rs+27\right)& =& {\left(rs\right)}^2-{27}^2\\ {\left(rs\right)}^2-{27}^2& =& r^2{s}^2-729\end{array}$