Question

Identify the property that justifies each step asked about in the answer area below. Line 1: , left parenthesis, 5, x, right parenthesis, left parenthesis, 2, y, right parenthesis Line 1: = (5x)(2y) Line 2: , 5, dot, left parenthesis, x, dot, 2, right parenthesis, dot, y Line 2: = 5⋅(x⋅2)⋅y Line 3: , 5, dot, left parenthesis, 2, dot, x, right parenthesis, dot, y Line 3: = 5⋅(2⋅x)⋅y Line 4: , left parenthesis, 5, dot, 2, right parenthesis, left parenthesis, x, dot, y, right parenthesis Line 4: = (5⋅2)(x⋅y) Line 5: , 10, x, y Line 5: = 10xy Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3: Line 3 to Line 4:

Answer 1

To identify the property that justifies each step in the transformations, we can consider the mathematical operations involved. Here’s the breakdown:

1. **Line 1 to Line 2**:
- Justification: **Associative Property of Multiplication**
- Explanation: This property allows us to regroup the factors being multiplied. Here, \( (5x)(2y) \) is regrouped as \( 5 \cdot (x \cdot 2) \cdot y \).

2. **Line 2 to Line 3**:
- Justification: **Commutative Property of Multiplication**
- Explanation: This property states that the order of multiplication does not change the product. In this case, \( 5 \cdot (x \cdot 2) \cdot y \) is reordered as \( 5 \cdot (2 \cdot x) \cdot y \).

3. **Line 3 to Line 4**:
- Justification: **Associative Property of Multiplication**
- Explanation: This again allows us to regroup the factors. Here, \( 5 \cdot (2 \cdot x) \cdot y \) is regrouped as \( (5 \cdot 2)(x \cdot y) \).

Overall, the justification for each step is rooted in the properties of multiplication: associative and commutative. The final step then simplifies to \( 10xy \) by calculating \( 5 \cdot 2 \).