Question

Identify the property that justifies each step asked about in the answer area below.
Line 1: (5x)(2y)
Line 2: 5⋅(x⋅2)⋅y
Line 3: 5⋅(2⋅x)⋅y
Line 4: (5⋅2)(x⋅y)
Line 5: 10xy

Answer 1

Certainly! Below are the properties that justify each step in the transformation:

**Line 1: (5x)(2y)**
- This is the original expression.

**Line 2: 5⋅(x⋅2)⋅y**
- **Property used:** Associative Property of Multiplication (rearranging the factors).

**Line 3: 5⋅(2⋅x)⋅y**
- **Property used:** Commutative Property of Multiplication (reordering the factors).

**Line 4: (5⋅2)(x⋅y)**
- **Property used:** Associative Property of Multiplication (grouping the factors).

**Line 5: 10xy**
- **Property used:** The product of the coefficients (Evaluating \(5 \cdot 2\) to get \(10\)) and bringing factors together.

So, the properties are:
1. **Associative Property**
2. **Commutative Property**
3. **Associative Property**
4. **Multiplication (Evaluating the product of constants)**

These provide a structured flow from the initial expression to the final result.