Question

Use the box method to distribute and simplify left parenthesis, 2, x, minus, 5, right parenthesis, left parenthesis, minus, 5, x, plus, 2, right parenthesis, .(2x−5)(−5x+2). Drag and drop the terms to the correct locations of the table.

Answer 1

To use the box method for distributing the expression \((2x - 5)(-5x + 2)\), we will create a 2x2 grid (box) to expand the expression. Here’s how to set up and fill out the box:

1. **Create a grid:** Each factor (term from the two binomials) will be a row and a column in the box.

```
| -5x | 2 |
-----------------
2x | | |
-----------------
-5 | | |
```

2. **Fill in the products:** Multiply each term in the rows by each term in the columns.

- **For the term \(2x\) and \(-5x\):**
\[
2x \cdot (-5x) = -10x^2
\]

- **For the term \(2x\) and \(2\):**
\[
2x \cdot 2 = 4x
\]

- **For the term \(-5\) and \(-5x\):**
\[
-5 \cdot (-5x) = 25x
\]

- **For the term \(-5\) and \(2\):**
\[
-5 \cdot 2 = -10
\]

Now, we can fill the box:

```
| -5x | 2 |
--------------------------
2x | -10x² | 4x |
--------------------------
-5 | 25x | -10 |
```

3. **Combine like terms:** Now we will combine all the products from the grid:

\[
-10x^2 + 4x + 25x - 10
\]

Combine \(4x\) and \(25x\):

\[
-10x^2 + 29x - 10
\]

Thus, the final result is:

\[
\boxed{-10x^2 + 29x - 10}
\]