Question

Which step contains an error using the Commutative Property of Addition in verifying 8 + x ^ 2 + 17x - x ^ 2 + 4 = 10 + 4x ^ 2 + 10x - 4x ^ 2 + 2 + 7x ? 601.8 + 4 + x ^ 2 - x ^ 2 + 17x = 10 + 2 + 10x - 4x ^ 2 + 7x + 4x ^ 2; los 2 8+4+17x+x^ 2 -x^ 2 =10+2+4x^ 2 -4x^ 2 +10x+7x Step 12 + 17x + x ^ 2 = 12 - x ^ 2 + 17x

Answer 1

Let's analyze the expression you provided and verify where the error using the Commutative Property of Addition might lie.

The original expression provided was:
\[ 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]

Let's simplify both sides.

### Left Side Simplification
Starting with the left side:
\[ 8 + x^2 + 17x - x^2 + 4 \]

1. Combine like terms:
- \( x^2 - x^2 = 0 \), so the \( x^2 \) terms cancel each other out.
- Combine constant terms: \( 8 + 4 = 12 \)

The left side simplifies to:
\[ 12 + 17x \]

### Right Side Simplification
For the right side:
\[ 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]

1. Combine like terms:
- \( 4x^2 - 4x^2 = 0 \), so the \( 4x^2 \) terms cancel each other out.
- Combine constant terms: \( 10 + 2 = 12 \)
- Combine linear terms: \( 10x + 7x = 17x \)

The right side simplifies to:
\[ 12 + 17x \]

### Conclusion
Both sides simplify to the same expression:
\[ 12 + 17x \]

Thus, we see that there doesn't appear to be an error in using the Commutative Property of Addition in the simplifications provided.

If we examine step-to-step verses as laid out:
- \( 601.8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
- If it was manipulated with different formats wrongfully or the rearrangement led to inconsistency that is not reflective in original decompositions, it could have created a fault.

The steps you provided ultimately balance out, based on distributed operations, showcasing equality throughout those alterations, affirming that Commutative Property usage matches.

Feel free to specify a particular step or reformat yours if further error allocations arise!