Chapter 4.6, Problem 7WE

To determine

To Multiply: the given expression

Answer to Problem 7WE

The expression we get after multiplying using vertical form is $\boxed{c^3-7c{d}^2+6d^3}$

Explanation of Solution

Given information: $\begin{array}{l}{c}^2+2cd-3d^2\\ \underset{\_}{c-2d}\end{array}$

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

  $\begin{array}{l}{c}^2+2cd-3d^2\\ \underset{\_}{c-2d}\\ -2c^{2}d-4c{d}^2+6d^3\to 1^{st}partialproduct\end{array}$

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

  $\begin{array}{l}{c}^2+2cd-3d^2\\ \underset{\_}{c-2d}\\ -2c^{2}d-4c{d}^2+6d^3\to 1^{st}partialproduct\\ c^3+2c^{2}d-3c{d}^2\to 2^{nd}partialproduct\end{array}$

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

  $\begin{array}{l}{c}^2+2cd-3d^2\\ \underset{\_}{c-2d}\\ -2c^{2}d-4c{d}^2+6d^3\to 1^{st}partialproduct\\ \underset{\_}{c^3+2c^{2}d-3c{d}^2\to 2^{nd}partialproduct}\\ c^3+0c^{2}d-7c{d}^2+6d^3\end{array}$

Conclusion:

The expression we get after multiplying using vertical form is $\boxed{c^3-7c{d}^2+6d^3}$