Chapter 8.3, Problem 26PPS

To determine

To find: The product $\left(4a+7\right)\left(9a^2+2a-7\right)$

Answer to Problem 26PPS

  $36a^3+71a^2-14a-49$

Explanation of Solution

Given:

  $\left(4a+7\right)\left(9a^2+2a-7\right)$

Calculation:

Multiply each term of the first polynomial with the each term of the second polynomial

  $\begin{array}{l}\left(4a+7\right)\left(9a^2+2a-7\right)\\ 4a\cdot 9a^2+4a\cdot 2a+4a\cdot \left(-7\right)+7\cdot 9a^2+7\cdot 2a+7\cdot \left(-7\right)\\ =36a^3+8a^2-28a+63a^2+14a-49\\ =36a^3+71a^2-14a-49\end{array}$

So, the product of the polynomial is $36a^3+71a^2-14a-49$