Use the box method to distribute and simplify (- 3x ^ 2 + 2x - 6)(- 2x - 4) .
Tell me where each of the numbers go like top right middle right bottom right right top left top
And the box is
3 rows 2 columns
To distribute and simplify (-3x^2 + 2x - 6)(-2x - 4) using the box method, we will set up a 3-row, 2-column box.
The box will look like:
_____|_________
_____|_________
_____|_________
Now, let's fill in the numbers:
-3x^2 will go in the top left cell.
2x will go in the middle left cell.
-6 will go in the bottom left cell.
-2x will go in the top right cell.
-4 will go in the middle right cell.
Now, let's multiply each number in the top row by each number in the bottom row, and fill in the corresponding cells:
_____|_______-2x_______
_____|__________________
_____|__________________
_____|_______4x^3______
_____|__________________
_____|__________________
_____|_______-12x______
_____|__________________
_____|__________________
Now, we have filled in the numbers using the box method. We can see that:
-3x^2 * -2x = 6x^3 (top right cell)
-3x^2 * -4 = 12x^2 (middle right cell)
2x * -2x = -4x^2 (top left cell)
2x * -4 = -8x (middle left cell)
-6 * -2x = 12x (bottom right cell)
-6 * -4 = 24 (bottom left cell)
Finally, we add up all the numbers in the box:
6x^3 - 4x^2 + 12x - 8x + 12x + 24
Combining like terms, we get:
6x^3 - 4x^2 + 16x + 24
Therefore, (-3x^2 + 2x - 6)(-2x - 4) simplifies to 6x^3 - 4x^2 + 16x + 24.