(x-3)-box-method.jpeg "(4x-5)(x-3) Box Method")
Using the Box Method to Multiply (4x - 5)(x - 3)
The box method is a visual way to multiply binomials, making it easy to keep track of terms and avoid mistakes. Here's how it works for multiplying (4x - 5)(x - 3):
1. Set up the Box
Draw a 2x2 box, representing the two terms in each binomial.
| x | -3 | |
|---|---|---|
| 4x | ||
| -5 |
2. Fill the Box
Multiply the terms along the rows and columns and fill each box with the product.
| x | -3 | |
|---|---|---|
| 4x | 4x² | -12x |
| -5 | -5x | 15 |
3. Combine Like Terms
Now, add the terms from the boxes that are like terms:
- 4x² (There's only one x² term)
- -12x - 5x = -17x (Combining the x terms)
- 15 (There's only one constant term)
4. Write the Final Product
Combining the terms, the product of (4x - 5)(x - 3) is 4x² - 17x + 15.
Advantages of the Box Method
- Organization: The box method helps you keep track of all the terms and avoid missing any.
- Visual Aid: It provides a visual representation of the multiplication process, making it easier to understand.
- Systematic: It follows a consistent pattern, making it easy to apply to any binomial multiplication.
The box method is a useful tool for multiplying binomials, especially for beginners. It simplifies the process and ensures accuracy.