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
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 |
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| | | |
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| -3x^2 | | |
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| 2x | | |
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| -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 |
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| 2x | -4x | -8x |
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| -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.