Q.235. - Intermediate Algebra

Question

Multiply each pair of conjugates using the product of the conjugates pattern.

$\left(p+\frac{4}{5}q\right)\left(p-\frac{4}{5}q\right)$

Step-by-Step Solution

Answer

The solution is $p^2-\frac{16}{25}{q}^2$.

Step 1. Given information.

The given expression is $\left(p+\frac{4}{5}q\right)\left(p-\frac{4}{5}q\right)$.

Step 2. Simplify the expression by using the difference of squares a + b a - b = a 2 - b 2 .

Solve it as follows:

$$\begin{gathered} \left(p+\frac{4}{5}q\right)\left(p-\frac{4}{5}q\right)={\left(p\right)}^2-{\left(\frac{4}{5}q\right)}^2 \\ \Rightarrow p^2-\frac{16}{25}{q}^2 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is $p^2-\frac{16}{25}{q}^2$.