Question
Identify the property that justifies each step asked about in the answer area below. Line 1: , left parenthesis, x, plus, 8, right parenthesis, left parenthesis, 3, plus, 10, x, right parenthesis Line 1: = (x+8)(3+10x) Line 2: , left parenthesis, x, plus, 8, right parenthesis, left parenthesis, 10, x, plus, 3, right parenthesis Line 2: = (x+8)(10x+3) Line 3: , left parenthesis, 10, x, plus, 3, right parenthesis, left parenthesis, x, plus, 8, right parenthesis Line 3: = (10x+3)(x+8) Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3:
Answers
GPT-4o mini
To justify the steps between the lines provided, we can identify the properties being used.
**Line 1 to Line 2:**
- **Property:** Commutative Property of Addition
- **Justification:** The order of the terms in the second factor is changed. Specifically, \(3 + 10x\) is rearranged as \(10x + 3\).
**Line 2 to Line 3:**
- **Property:** Commutative Property of Multiplication
- **Justification:** The order of the factors is switched. The factors \((x + 8)\) and \((10x + 3)\) are swapped to become \((10x + 3)(x + 8)\).
So, the final answers for your justification are:
- Line 1 to Line 2: Commutative Property of Addition
- Line 2 to Line 3: Commutative Property of Multiplication
**Line 1 to Line 2:**
- **Property:** Commutative Property of Addition
- **Justification:** The order of the terms in the second factor is changed. Specifically, \(3 + 10x\) is rearranged as \(10x + 3\).
**Line 2 to Line 3:**
- **Property:** Commutative Property of Multiplication
- **Justification:** The order of the factors is switched. The factors \((x + 8)\) and \((10x + 3)\) are swapped to become \((10x + 3)(x + 8)\).
So, the final answers for your justification are:
- Line 1 to Line 2: Commutative Property of Addition
- Line 2 to Line 3: Commutative Property of Multiplication