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:
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| | | 4x | 3 |
|---|---|----|---|
| 5x| | | |
| 2 | | | |
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Now we will distribute the terms:
To fill in the top left box, we multiply 5x by 4x, which gives us 20x².
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| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| | |
| 2 | | | |
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To fill in the top right box, we multiply 5x by 3, which gives us 15x.
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| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| |
| 2 | | | |
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To fill in the bottom left box, we multiply 2 by 4x, which gives us 8x.
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| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| |
| 2 | 8x | | |
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Lastly, to fill in the bottom right box, we multiply 2 by 3, which gives us 6.
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| | | 4x | 3 |
|---|---|----|---|
| 5x| 20x²| 15x| 6 |
| 2 | 8x | | |
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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
Use the box method to distribute and simplify (5x + 2)(4x + 3) Drag and drop the terms to the correct locations of the table.
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