(x-4)(x+7)

Using the box method

To use the box method, we will create a box with two columns and two rows.

In the first row, we will write down the factors of x-4 and x+7.
In the first column, we will write down the factors of x-4.

The factors of x-4 are x and -4, so we write them in the first column:

x
___________
x | x^2
| -4x
In the second column, we will write down the factors of x+7:

x + 7
___________
x | x^2 + 7x
| -4x + 28

After multiplying the factors in each cell, we add up the terms:

x^2 + 7x - 4x + 28

Simplifying the expression by combining like terms:

x^2 + 3x + 28

Therefore, the expansion of (x-4)(x+7) using the box method is x^2 + 3x + 28.