Use the box method to distribute and simplify left bracket, 2, x, plus, 6, right bracket, left bracket, minus, 4, x, minus, 4, right bracket, .(2x+6)(−4x−4). Drag and drop the terms to the correct locations of the table.
left bracket(2, x2xplus+66right bracket)left bracket(minus−4, x4xminus−44right bracket)
The box method is a way to distribute and simplify expressions. Here's how it works:
1. Draw a box with two columns and two rows.
2. Write the terms of one expression along the top of the box, and the terms of the other expression along the side of the box.
3. Multiply each term in the top row with each term in the side column, and write the results in the corresponding cells of the box.
4. Simplify each cell by combining like terms.
5. Add or subtract the simplified cells to get the final answer.
Here's how the box method would look for the expression (2x + 6)(-4x - 4):
```
____________________________
| | -4x | -4 |
| 2x | -8x^2 | -8x |
| 6 | -24x | -24 |
```
In the cells of the box, we multiply each term from the top row with each term from the side column. For example, in the top left cell, we have 2x * -4x = -8x^2.
Now, let's simplify each cell:
-8x^2: There are no like terms to combine.
-8x + (-24x) = -32x: Combine like terms.
-8x + (-24) = -32: Combine like terms.
Finally, we add or subtract the simplified cells:
(-8x^2) + (-32x) + (-32) = -8x^2 - 32x - 32
So, using the box method, we distributed and simplified the expression (2x + 6)(-4x - 4) to get -8x^2 - 32x - 32.