can you just put 1,2,3,4 for each answer you give me so i know what number option it is? thanks!

Question

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

GPT-4o mini · Answer

To simplify the expression (9m - 3) - (2m + 12), we follow these steps:

Distribute the negative sign:
(9m - 3) - (2m + 12) = 9m - 3 - 2m - 12
Combine like terms:
(9m - 2m) + (-3 - 12) = 7m - 15

So the simplified expression is:

2. 7m - 15

Answer

Simplify the expression below (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

GPT-4o mini · Answer

To simplify the expression (2x + 4)(7x - 1), we use the distributive property (also known as the FOIL method for binomials):

Multiply the first terms:
$2x \cdot 7x = 14x^2$
Multiply the outer terms:
$2x \cdot -1 = -2x$
Multiply the inner terms:
$4 \cdot 7x = 28x$
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

Answer

**WRITTEN RESPONSE** Simplify the expression using the Distributive Property: 7(2x+4) = (1 point)

GPT-4o mini · Answer

To simplify the expression $ 7(2x + 4) $ using the Distributive Property, we multiply $ 7 $ by each term inside the parentheses: 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**

Answer

**WRITTEN RESPONSE** Rewrite the following expression using the Commutative Property of Multiplication. Make sure you use the parenthesis correctly! (2×3n)+11 = (1 point)

GPT-4o mini · Answer

Using the Commutative Property of Multiplication, which states that $a \cdot b = b \cdot a$, we can rewrite the expression $(2 \times 3n) + 11$.

By changing the order of multiplication, we can express it as:

\[ (3n \times 2) + 11 \]

So the rewritten expression is:

(3n × 2) + 11

Answer

**WRITTEN RESPONSE**
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)

GPT-4o mini · Answer

Sara's friend should check her solution step by step to ensure that each operation is performed correctly. Let's analyze the steps provided.

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 $-3x^3 + 2x^2 - 5x$."