Question

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

$\left(7w+10x\right)\left(7w-10x\right)$

Short answer

The solution is$49w^2-100x^2$.

Step-by-step solution

Step 1. Given information.

The given expression is$\left(7w+10x\right)\left(7w-10x\right)$.

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

Solve it as follows:

$$\begin{gathered} \left(7w+10x\right)\left(7w-10x\right)={\left(7w\right)}^2-{\left(10x\right)}^2 \\ \Rightarrow 49w^2-100x^2 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is$49w^2-100x^2$.