Question

Use the box method to distribute and simplify (5x + 2)(4x + 3) Drag and drop the terms to the correct locations of the table.

Answer 1

To use the box method, we will distribute each term of the first expression (5x + 2) to each term of the second expression (4x + 3).

First, let's set up the box method table:

-----------------------------
| | | 4x | 3 |
|---|---|----|---|
| 5x| | | |
| 2 | | | |
-----------------------------

Now we will distribute the terms:

To fill in the top left box, we multiply 5x by 4x, which gives us 20x².

-----------------------------
| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| | |
| 2 | | | |
-----------------------------

To fill in the top right box, we multiply 5x by 3, which gives us 15x.

-----------------------------
| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| |
| 2 | | | |
-----------------------------

To fill in the bottom left box, we multiply 2 by 4x, which gives us 8x.

-----------------------------
| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| |
| 2 | 8x | | |
-----------------------------

Lastly, to fill in the bottom right box, we multiply 2 by 3, which gives us 6.

-----------------------------
| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| 6 |
| 2 | 8x | | |
-----------------------------

So, the simplified form after distributing and using the box method is:

(5x + 2)(4x + 3) = 20x² + 15x + 8x + 6

Now, we can rearrange the terms to simplify further:

(5x + 2)(4x + 3) = 20x² + (15x + 8x) + 6

Simplifying the expression within the parentheses, we get:

(5x + 2)(4x + 3) = 20x² + 23x + 6