Chapter 14.4, Problem 30HP

To determine

To find:the three different multiplication problems for the given product.

Answer to Problem 30HP

  $6a^2+8a=2a\left(3a+4\right)=a\left(6a+8\right)=2\left(3a^2+4\right)$

Explanation of Solution

Given:

The given product: $6a^2+8a$

Calculation:

As thegiven product is $6a^2+8a$ .

Now, it is to find the three different multiplication problems for the given product.

Since, $6a^2$ is expanded as $\left(3a\times 2a\right)$

And $8a$ is expanded as $\left(4\times 2a\right)$

Therefore, the different multiplication problems are:

  $\begin{array}{l}6a^2+8a=3a\times 2a+4\times 2a\\ =2a\left(3a+4\right)\left\{first\right\}\\ 6a^2+8a=a\times 6a+a\times 8\\ =a\left(6a+8\right)\left\{second\right\}\\ 6a^2+8a=2\times 3a^2+2\times 4a\\ =2\left(3a^2+4\right)\left\{third\right\}\end{array}$

Hence, the three different multiplication problems for the given productis $6a^2+8a=2a\left(3a+4\right)=a\left(6a+8\right)=2\left(3a^2+4\right)$ .