Simplify the expression
(9m-3) - (2m+12)
(1 point)
Responses
18m2−36
18 m squared minus 36
7m - 15
7m - 15
7m+9
7m+9
11m - 15
Bot GPT 4-o mini
answered
1. Distribute the negative sign:
(9m - 3) - (2m + 12) = 9m - 3 - 2m - 12
2. Combine like terms:
(9m - 2m) + (-3 - 12) = 7m - 15
So the simplified expression is:
**2. 7m - 15**
anonymous
answered
(2x+4)(7x-1)
(1 point)
Responses
9x2−26x−4
9 x squared minus 26 x minus 4
9x - 4
9x - 4
14x2−26x−4
14 x squared minus 26 x minus 4
14x2−30x−4
Bot GPT 4-o mini
answered
1. Multiply the first terms:
\(2x \cdot 7x = 14x^2\)
2. Multiply the outer terms:
\(2x \cdot -1 = -2x\)
3. Multiply the inner terms:
\(4 \cdot 7x = 28x\)
4. Multiply the last terms:
\(4 \cdot -1 = -4\)
Now, combine all these results:
\(14x^2 - 2x + 28x - 4\)
Combine like terms:
\(14x^2 + 26x - 4\)
So, the simplified expression is:
**3. 14x² - 26x - 4**
anonymous
answered
Simplify the expression using the Distributive Property:
7(2x+4) =
(1 point)
Bot GPT 4-o mini
answered
1. \( 7 \cdot 2x = 14x \)
2. \( 7 \cdot 4 = 28 \)
Now, combine the results:
\[
7(2x + 4) = 14x + 28
\]
So the simplified expression is:
**14x + 28**
anonymous
answered
Rewrite the following expression using the Commutative Property of Multiplication. Make sure you use the parenthesis correctly!
(2×3n)+11 =
(1 point)
Bot GPT 4-o mini
answered
By changing the order of multiplication, we can express it as:
\[
(3n \times 2) + 11
\]
So the rewritten expression is:
**(3n × 2) + 11**
anonymous
answered
Sara subtracted two polynomials. She asked a friend to check her solution and work. What should her friend tell her? Is Sara correct? If she is not correct, explain which step the error was made AND what the error was.
(2x3−7x2+4x)−(9x−5x3+9x2)
Step 1: 2x3−7x2+4x−9x−5x3+9x2
Step 2: 2x3−5x3−7x2+9x2+4x−9x
Step 3: −3x3+2x2−5x
(2 points)
Bot GPT 4-o mini
answered
### Given expression:
\((2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)\)
### Step 1:
Sara rewrote the expression as:
\[ 2x^3 - 7x^2 + 4x - 9x - 5x^3 + 9x^2 \]
**This step is correct.** She appropriately distributed the negative sign.
### Step 2:
Sara rearranged the terms to combine them:
\[ 2x^3 - 5x^3 - 7x^2 + 9x^2 + 4x - 9x \]
**This step is also correct.** She properly grouped the like terms (although the order doesn't affect the result).
### Step 3:
Sara simplified the expression to:
\[ -3x^3 + 2x^2 - 5x \]
**This step contains an error.**
### Error:
- In combining the \(x^2\) terms, she computed \( -7x^2 + 9x^2 \) incorrectly. The correct calculation should be:
\[
-7x^2 + 9x^2 = 2x^2
\]
- However, the subtraction of the \(x\) terms \(4x - 9x\) is correctly calculated as \(-5x\).
So, the total from Step 3 should be:
\[
-3x^3 + 2x^2 - 5x
\]
**Final Conclusion:**
Sara's friend should tell her that the steps were mostly correct, but she should double-check her calculations. If we specifically focus on the polynomials, she needs to ensure she correctly combines like terms. In this case, **there was no error** in Step 3, as her final answer of \(-3x^3 + 2x^2 - 5x\) is indeed correct.
**Final Answer to Friend's Response:**
"Sara, your solution is correct. The way you subtracted and combined the terms is accurate. There was no error in your steps. You have calculated the final expression correctly as \(-3x^3 + 2x^2 - 5x\)."
