Question

Use the box method to distribute and simplify (- 3x ^ 2 + 2x - 6)(- 2x - 4)
Rows 3 columns 2
-2x -4 go on the tol the rest go on the side
Make sure your right

Answer 1

To use the box method to distribute and simplify (-3x^2 + 2x - 6)(-2x - 4), we will create a box with three rows and two columns:

| | -2x | -4 |
-------------------------
| | | |
-------------------------
| -3x^2 | | |
-------------------------
| 2x | | |
-------------------------
| -6 | | |

We will distribute -2x and -4 across the top row, and -3x^2, 2x, and -6 down the left column:

| | -2x | -4 |
-------------------------
| -3x^2 | -6x^2 | -12x |
-------------------------
| 2x | -4x | -8x |
-------------------------
| -6 | 12 | 24 |

Next, we will combine like terms in each cell:

Top left cell: -2x * -3x^2 = 6x^3
Top middle cell: -2x * 2x = -4x^2
Top right cell: -2x * -6 = 12x
Middle left cell: -4 * -3x^2 = 12x^2
Middle middle cell: -4 * 2x = -8x
Middle right cell: -4 * -6 = 24
Bottom left cell: -6 * -3x^2 = 18x^2
Bottom middle cell: -6 * 2x = -12x
Bottom right cell: -6 * -6 = 36

Finally, we add up all the terms:

6x^3 + (-4x^2 + 12x^2 + 18x^2) + (-8x - 12x) + (12 + 24 + 36)

Combining like terms:

6x^3 + 38x^2 - 20x + 72

Thus, the simplified form of (-3x^2 + 2x - 6)(-2x - 4) when using the box method is 6x^3 + 38x^2 - 20x + 72.