Q.237. - Intermediate Algebra

Question

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

$\left(xy-9\right)\left(xy+9\right)$

Step-by-Step Solution

Answer

The solution is $x^2{y}^2-81$.

Step 1. Given information.

The given expression is $\left(xy-9\right)\left(xy+9\right)$.

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

Solve it as follows:

$$\begin{gathered} \left(xy-9\right)\left(xy+9\right)={\left(xy\right)}^2-{\left(9\right)}^2 \\ \Rightarrow x^2{y}^2-81 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is $x^2{y}^2-81$.