Question

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

$\left(ab-4\right)\left(ab+4\right)$

Short answer

The solution is$a^2{b}^2-16$.

Step-by-step solution

Step 1. Given information.

The given expression is$\left(ab-4\right)\left(ab+4\right)$.

Step 2. Simplify the expression by using the difference of squares a+ba-b=a2-b2.

Solve it as follows:

$$\begin{gathered} \left(ab-4\right)\left(ab+4\right)={\left(ab\right)}^2-{\left(4\right)}^2 \\ \Rightarrow a^2{b}^2-16 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is$a^2{b}^2-16$.