Question

Identify the property that justifies each step asked about in the answer area below. Line 1: , left parenthesis, x, plus, 10, right parenthesis, left parenthesis, 9, plus, 4, x, right parenthesis Line 1: = (x+10)(9+4x) Line 2: , left parenthesis, x, plus, 10, right parenthesis, left parenthesis, 4, x, plus, 9, right parenthesis Line 2: = (x+10)(4x+9) Line 3: , left parenthesis, 4, x, plus, 9, right parenthesis, left parenthesis, x, plus, 10, right parenthesis Line 3: = (4x+9)(x+10) Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3:

Answer 1

To identify the properties that justify each step, we can look at the transformations applied to the expressions.

### Line 1 to Line 2:
From Line 1: \((x + 10)(9 + 4x)\) to Line 2: \((x + 10)(4x + 9)\)

**Justification:**
This step involves rearranging the terms inside the second factor. This is justified by the **Commutative Property of Addition**, which states that the order in which two numbers are added does not change the sum.

### Line 2 to Line 3:
From Line 2: \((x + 10)(4x + 9)\) to Line 3: \((4x + 9)(x + 10)\)

**Justification:**
This step switches the factors without changing their product. This is justified by the **Commutative Property of Multiplication**, which states that the order in which two numbers are multiplied does not change the product.

### Summary:
- **Line 1 to Line 2:** Commutative Property of Addition
- **Line 2 to Line 3:** Commutative Property of Multiplication