Chapter 4.6, Problem 13ST

To determine

To Multiply: the given expression

Answer to Problem 13ST

The expression we get after multiplying using vertical form is $\boxed{5a^3+11a^2-2a-8}$

Explanation of Solution

Given information: $\begin{array}{l}{a}^2+3a+2\\ \underset{\_}{5a-4}\end{array}$

Concept Involved:

Multiply the second term of the bottom row with first row to get the 1^st partial product, then multiply the first term of bottom row with first row to get 2^nd partial product, then add the results of 1^st partial product and 2^nd partial product to get the final answer.

Calculation:

Multiplying -4 with first row to get the 1^st partial product

  $\begin{array}{l}{a}^2+3a+2\\ \underset{\_}{5a-4}\\ -4a^2-12a-8\to 1^{st}partialproduct\end{array}$

Multiplying 5a with the second row to the 2^nd partial product

  $\begin{array}{l}{a}^2+3a+2\\ \underset{\_}{5a-4}\\ -4a^2-12a-8\to 1^{st}partialproduct\\ 5a^3+15a^2+10a\to 2^{nd}partialproduct\end{array}$

Add the 1^st and 2^nd partial product to get the final answer

  $\begin{array}{l}{a}^2+3a+2\\ \underset{\_}{5a-4}\\ -4a^2-12a-8\to 1^{st}partialproduct\\ \underset{\_}{5a^3+15a^2+10a\to 2^{nd}partialproduct}\\ 5a^3+11a^2-2a-8\end{array}$

Conclusion:

The expression we get after multiplying using vertical form is $\boxed{5a^3+11a^2-2a-8}$