Identify the property that justifies each step asked about in the answer area below.

Question

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.