Chapter 4.6, Problem 5WE

To determine

To Multiply: the given expression

Answer to Problem 5WE

The expression we get after multiplying using vertical form is $\boxed{6x^2+11xy-10y^2}$

Explanation of Solution

Given information: $\begin{array}{l}3x-2y\\ \underset{\_}{2x+5y}\end{array}$

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 5y with first row to get the 1^st partial product

  $\begin{array}{l}3x-2y\\ \underset{\_}{2x+5y}\\ 15xy-10y^2\to 1^{st}partialproduct\end{array}$

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

  $\begin{array}{l}3x-2y\\ \underset{\_}{2x+5y}\\ 15xy-10y^2\to 1^{st}partialproduct\\ 6x^2-4xy\to 2^{nd}partialproduct\end{array}$

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

  $\begin{array}{l}3x-2y\\ \underset{\_}{2x+5y}\\ 15xy-10y^2\to 1^{st}partialproduct\\ \underset{\_}{6x^2-4xy\to 2^{nd}partialproduct}\\ 6x^2+11xy-10y^2\end{array}$

Conclusion:

The expression we get after multiplying using vertical form is $\boxed{6x^2+11xy-10y^2}$