Chapter 8.4, Problem 39PPS

To determine

To find: The product $\left(8a^2-9b^3\right)\left(8a^2+9b^3\right)$

Answer to Problem 39PPS

  $64a^4-81b^6$

Explanation of Solution

Given:

  $\left(8a^2-9b^3\right)\left(8a^2+9b^3\right)$

Calculation:

The given expression is $\left(8a^2-9b^3\right)\left(8a^2+9b^3\right)$

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

  $\begin{array}{l}\left(8a^2-9b^3\right)\left(8a^2+9b^3\right)\\ ={\left(8a^2\right)}^2-{\left(9b^3\right)}^2\\ =64a^4-81b^6\end{array}$