Q.234. - Intermediate Algebra

Question

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

$\left(m+\frac{2}{3}n\right)\left(m-\frac{2}{3}n\right)$

Step-by-Step Solution

Answer

The solution is $m^2-\frac{4}{9}{n}^2$.

Step 1. Given information.

The given expression is $\left(m+\frac{2}{3}n\right)\left(m-\frac{2}{3}n\right)$.

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

Solve it as follows:

$$\begin{gathered} \left(m+\frac{2}{3}n\right)\left(m-\frac{2}{3}n\right)={\left(m\right)}^2-{\left(\frac{2}{3}n\right)}^2 \\ \Rightarrow m^2-\frac{4}{9}{n}^2 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is $m^2-\frac{4}{9}{n}^2$.