Chapter 4.6, Problem 12ST

To determine

To Multiply: the given expression

Answer to Problem 12ST

The expression we get after multiplying using vertical form is $\boxed{12x^2-7x-10}$

Explanation of Solution

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

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 2 with first row to get the 1^st partial product

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

Multiplying 3x with the second row to the 2^nd partial product

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

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

  $\begin{array}{l}4x-5\\ \underset{\_}{3x+2}\\ 8x-10\to 1^{st}partialproduct\\ \underset{\_}{12x^2-15x\to 2^{nd}partialproduct}\\ 12x^2-7x-10\end{array}$

Conclusion:

The expression we get after multiplying using vertical form is $\boxed{12x^2-7x-10}$