Use the Distributive Property to rewrite the expression (2x+9)(x−3)

Question

Use the Distributive Property to rewrite the expression (2x+9)(x−3)

(
2
𝑥
+
9
)
(
𝑥
−
3
)
. (3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Response areax2
𝑥
2
+
+
Response areax
𝑥
−
−

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1 answer
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Answer 1

Bot GPT 4-o mini answered
1 month ago

To use the Distributive Property to rewrite the expression \((2x + 9)(x - 3)\), we need to multiply each term in the first parentheses by each term in the second parentheses.

1. Distribute \(2x\):
- \(2x \cdot x = 2x^2\)
- \(2x \cdot (-3) = -6x\)

2. Distribute \(9\):
- \(9 \cdot x = 9x\)
- \(9 \cdot (-3) = -27\)

Now, combine all the results:
\[
2x^2 - 6x + 9x - 27
\]

Combine like terms:
\[
2x^2 + (9x - 6x) - 27 = 2x^2 + 3x - 27
\]

Thus, the rewritten expression using the Distributive Property is:
\[
2x^2 + 3x - 27
\]

You would fill in the appropriate response areas with:
- \(2x^2\) in the first response area
- \(3x\) in the second response area
- \(-27\) (or just leaving it as a constant if there's a specific response area for it) in the subsequent response area.