Q.232. - Intermediate Algebra

Question

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

$\left(9c-2d\right)\left(9c+2d\right)$

Step-by-Step Solution

Answer

The solution is $81c^2-4d^2$.

Step 1. Given information.

The given expression is $\left(9c-2d\right)\left(9c+2d\right)$.

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

Solve it as follows:

$$\begin{gathered} \left(9c-2d\right)\left(9c+2d\right)={\left(9c\right)}^2-{\left(2d\right)}^2 \\ \Rightarrow 81c^2-4d^2 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is $81c^2-4d^2$.