Write the product in standard form.  Use the box to multiply.
( x - 4 ) ( 2x + 5 )

To multiply \((x - 4)(2x + 5)\) using the box method, we first set up a 2x2 grid, placing the terms of each binomial on the sides of the grid.

### Step 1: Set up the box
- The first binomial is \(x - 4\). Place \(x\) and \(-4\) on the top.
- The second binomial is \(2x + 5\). Place \(2x\) and \(5\) on the side.

|         | \(x\)  | \(-4\)  |
|---------|--------|---------|
| \(2x\)  | \(2x^2\) | \(-8x\) |
| \(5\)   | \(5x\)  | \(-20\)  |

### Step 2: Multiply each cell in the box
- Multiply \(x\) by \(2x\): \(2x^2\)
- Multiply \(x\) by \(5\): \(5x\)
- Multiply \(-4\) by \(2x\): \(-8x\)
- Multiply \(-4\) by \(5\): \(-20\)

### Step 3: Combine like terms
The terms from the box are \(2x^2\), \(5x\), \(-8x\), and \(-20\). Combine the like terms:

\[
2x^2 + (5x - 8x) - 20 = 2x^2 - 3x - 20
\]

### Final Answer:
The product in standard form is:
\[
2x^2 - 3x - 20
\]

Would you like more details on this process or have any questions?

Here are 5 related questions you could explore:
1. How do you use the distributive property to expand binomials?
2. How does the box method compare to the FOIL method for multiplying binomials?
3. Can the box method be used for polynomials with more than two terms?
4. What happens if both binomials have negative terms?
5. How do you factor a quadratic like \(2x^2 - 3x - 20\) after expanding?

**Tip:** When multiplying binomials, always remember to combine like terms carefully to avoid errors.

Write the product in standard form. Use the box to multiply. (x - 4)(2x + 5)

Learn how to multiply the binomials (x - 4)(2x + 5) using the box method and find the product in standard form. This problem involves key algebraic concepts like polynomial multiplication and the distributive property, suitable for students in Grades 8-10.

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