Chapter 8.4, Problem 27PPS

To determine

To find: The product $\left(3a^2+7b\right)\left(3a^2-7b\right)$

Answer to Problem 27PPS

  $9a^4-49b^2$

Explanation of Solution

Given:

  $\left(3a^2+7b\right)\left(3a^2-7b\right)$

Calculation:

The given expression is $\left(3a^2+7b\right)\left(3a^2-7b\right)$

Apply the formula $\left(a+b\right)\left(a-b\right)=a^2-b^2$ and then simplify

  $\begin{array}{l}\left(3a^2+7b\right)\left(3a^2-7b\right)\\ ={\left(3a^2\right)}^2-{\left(7b\right)}^2\\ =9a^4-49b^2\end{array}$