Q.236. - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The solution is $a^2{b}^2-16$.

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 + b a - b = a 2 - b 2 .

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 $a^2{b}^2-16$.