Chapter 8.4, Problem 48PPE

To determine

To simplify the product $\left(2p^2+7q\right)\left(2p^2-7q\right)$ .

Answer to Problem 48PPE

  $\left(2p^2+7q\right)\left(2p^2-7q\right)=4p^4-49q^2$

Explanation of Solution

Given:

  $\left(2p^2+7q\right)\left(2p^2-7q\right)$

Concept used:

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

Calculation:

  $\begin{array}{l}\left(2p^2+7q\right)\left(2p^2-7q\right)={\left(2p^2\right)}^2-{\left(7q\right)}^2\\ =4p^4-49q^2\end{array}$