Chapter 4.6, Problem 6WE

To determine

To Multiply: the given expression

Answer to Problem 6WE

The expression we get after multiplying using vertical form is $\boxed{2a^2-11ab+15b^2}$

Explanation of Solution

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

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 - 3b with first row to get the 1^st partial product

  $\begin{array}{l}2a-5b\\ \underset{\_}{a-3b}\\ -6ab+15b^2\to 1^{st}partialproduct\end{array}$

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

  $\begin{array}{l}2a-5b\\ \underset{\_}{a-3b}\\ -6ab+15b^2\to 1^{st}partialproduct\\ 2a^2-5ab\to 2^{nd}partialproduct\end{array}$

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

  $\begin{array}{l}2a-5b\\ \underset{\_}{a-3b}\\ -6ab+15b^2\to 1^{st}partialproduct\\ \underset{\_}{2a^2-5ab\to 2^{nd}partialproduct}\\ 2a^2-11ab+15b^2\end{array}$

Conclusion:

The expression we get after multiplying using vertical form is $\boxed{2a^2-11ab+15b^2}$