Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x? 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 3 Step 3 Step 1 Step 1 Step 2 Step 2 No mistake was made.

Answer 1

To identify where the error using the Commutative Property of Addition occurs, let's analyze the steps in detail.

1. Step 1:

   • Original expression: \( 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \)
   • Simplified: \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
   • This step appears to rearrange and group correctly according to the Commutative Property.

2. Step 2:

   • Simplified version: \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
   • Here, the simplification seems valid, but it seems the order of terms was not fully rearranged correctly (from the left original expression to correctly match the right side).

3. Step 3:

   • This gives us: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
   • Here, combining like terms seems to have introduced the term "\(-x^2\)" incorrectly because \(x^2 - x^2\) cancels out on the left side.

Therefore, the actual mistake occurs in Step 3, where the resulting equation incorrectly shows \(-x^2\) instead of simplifying fully.

Final answer: Step 3.