Question

Use the box method to distribute and simplify left parenthesis, 5, x, plus, 6, right parenthesis, left parenthesis, x, minus, 3, right parenthesis, .(5x+6)(x−3). Drag and drop the terms to the correct locations of the table.
left parenthesis(5, x5xplus+66right parenthesis)left parenthesis(xxminus−33right parenthesis)

Answer 1

To use the box method for distributing the expression \((5x + 6)(x - 3)\), we start by creating a table (or box) where we split each polynomial into rows and columns based on its terms.

### Step 1: Create the Box
We'll have two rows (for the first polynomial \(5x + 6\)) and two columns (for the second polynomial \(x - 3\)).

- Rows: \(5x\) and \(6\)
- Columns: \(x\) and \(-3\)

### Step 2: Fill the Box
Now we fill in each box by multiplying the terms from the corresponding row and column.

| | \(x\) | \(-3\) |
|----------|------------|------------|
| \(5x\) | \(5x \cdot x = 5x^2\) | \(5x \cdot -3 = -15x\) |
| \(6\) | \(6 \cdot x = 6x\) | \(6 \cdot -3 = -18\) |

### Step 3: Collect All Products
Now we combine these results:

- From the first row: \(5x^2 - 15x\)
- From the second row: \(6x - 18\)

### Step 4: Combine Like Terms
Now we combine the like terms from the results:

\[
5x^2 - 15x + 6x - 18
\]

Combine the \(x\) terms:

\[
-15x + 6x = -9x
\]

So, the final expression simplifies to:

\[
5x^2 - 9x - 18
\]

### Summary
To summarize, using the box method, we distributed and simplified \((5x + 6)(x - 3)\) to arrive at:

\[
\boxed{5x^2 - 9x - 18}
\]