Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x ?

Question

Step 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2

Step 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x

Step 3: 12+17x+x2=12−x2+17x

(1 point)
Responses

Step 2
Step 2

Step 3
Step 3

Step 1
Step 1

No mistake was made.

Answer 1

To identify the error using the Commutative Property of Addition, let's analyze each step.

Step 1:

\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)

Step 2:

\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)

In Step 2, the left side simplifies correctly to \( 12 + 17x \) because the \( x^2 - x^2 \) cancels out and \( 8 + 4 = 12 \).

However, on the right side of Step 2, \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \) simplifies incorrectly. The \( 4x^2 - 4x^2 \) cancels out, but when combined, \( 10x + 7x \) becomes \( 17x \), not \( -x^2 + 17x \).

Step 3:

In Step 3, it represents the conclusion that both sides simplify to \( 12 + 17x \).

Conclusion:

The mistake occurs in Step 2.

So, the answer is:

Step 2