Question

A teacher received the following answer to a quiz question in which the student was asked to simplify the expression in Step 1:

Step 1: −5(x − 16y) + 7(−2x − 8y)

Step 2: −5x + 80y − 14x − 8y

Step 3: −5x − 14x + 80y − 8y

Step 4: (−14x − 5x) + (80y − 8y)

Step 5: −19x + 72y


Part A: Identify the step where the student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. (6 points)


Part B: How would you correct the mistake? Show all your work. (6 points)


PLS HELP THIS IS DUE SOON :(

Answer 1

A) Step 2

B) Step 2 (corrected): -5x + 80y - 14x - 56y

Explanation:

Part A

The mistake made by the student occurs in Step 2.

In this step, the student did not distribute +7 to the second term (-8y) inside the parentheses. This is a distributive property error.

The distributive property states that when you multiply a number (or term) outside parentheses by the sum or difference inside the parentheses, you must distribute that number to each term inside the parentheses.

Part B

To correct the mistake made in Step 2, we need to correctly distribute +7 to both terms inside the parentheses.

Step 1: -5(x - 16y) + 7(-2x - 8y)

Step 2 (Corrected): -5x + 80y - 14x - 56y (Distribute +7 to -8y correctly)

From here, we can continue with the correct simplification:

Step 3: -5x - 14x + 80y - 56y

Step 4: (-5x - 14x) + (80y - 56y)

Step 5: -19x + 24y

Therefore, the final simplified expression is -19x + 24y.

Answer 2

See Below

Explanation:

Part A: The student made a disturbing mistake in Step 2. The specific error is that the student did not distribute the 7 with the 8y. This is a very serious mistake, as it shows that the student does not understand the basic concept of distribution.

Distributing a number with another number means multiplying each term inside the parentheses by the number outside the parentheses.

In this case, we need to multiply the 7 by the 8y inside the parentheses.

Correct Step 2:

-5(x - 16y) + 7(-2x -8y ) = -5x + 80y -14x - 56 y

This is the correct Step 2.

Part B: To correct the mistake, the student should distribute the 7 with the 8y in Step 2. This will give them the correct Step 2, which is:

-5x + 80y -14x - 56 y

Once they have the correct Step 2, they can simplify the expression by combining the like terms to get the correct answer at step 5.

Step 3: −5x − 14x + 80y − 56y

Step 4: (−14x − 5x) + (80y − 56y)

Step 5: −19x + 24y