Use the box method to distribute and simplify (- 3x ^ 2 + 2x - 6)(- 2x - 4) Drag and drop the terms to the correct locations of the table.
You can help me so don't even try it just use the line things and make it as accurate as you can
I'm sorry, but as a text-based AI, I am unable to create visual representations or use drag-and-drop features. However, I can guide you on how to solve this problem using the box method.
To distribute and simplify the expression (-3x^2 + 2x - 6)(-2x - 4) using the box method, follow these steps:
Step 1: Draw a box with two columns and two rows.
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Step 2: Split the expression into four parts and place them in the box.
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| -3x^2 | 2x |
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| -6 | -2x -4|
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```
Step 3: Multiply each term in the first row with each term in the second row.
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| 6x^2 | -12x |
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| 18x |....(1)..... |
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```
Step 4: Sum up all the expressions to get the simplified form.
(6x^2 - 12x) + (18x) + (-(2x)) + (-4) = 6x^2 + 4x - 4
Therefore, the simplified expression is 6x^2 + 4x - 4.
Apologies again for the limitations in visual representation. If you have any further questions, feel free to ask!
(-3x^2 + 2x - 6)(-2x - 4)
checking
-2x (-3x^2 + 2x - 6) -4 (-3x^2 + 2x - 6)
= 6 x^3 - 4 x^2 + 12 x + 12 x^2 -4 x + 24
= 6 x^3 + 8 x^2 + 8 x + 24
Apologies for the confusion. Let's go through the multiplication and simplification steps more accurately:
To distribute and simplify the expression (-3x^2 + 2x - 6)(-2x - 4):
Step 1: Multiply -2x by each term inside the first parentheses:
-2x * -3x^2 = 6x^3
-2x * 2x = -4x^2
-2x * -6 = 12x
Step 2: Multiply -4 by each term inside the first parentheses:
-4 * -3x^2 = 12x^2
-4 * 2x = -8x
-4 * -6 = 24
Step 3: Combine all the like terms:
6x^3 - 4x^2 + 12x + 12x^2 - 8x + 24
Combine the x^2 terms: -4x^2 + 12x^2 = 8x^2
Combine the x terms: 12x + (-8x) = 4x
The simplified expression is: 6x^3 + 8x^2 + 4x + 24.
I apologize for any confusion caused earlier. If you have any further questions, please let me know!