Question
Identify the property that justifies each step asked about in the answer area below.
Line 1: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 9, plus, 4, x, right parenthesis
Line 1: =
(x+6)(9+4x)
Line 2: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 4, x, plus, 9, right parenthesis
Line 2: =
(x+6)(4x+9)
Line 3: , left parenthesis, 4, x, plus, 9, right parenthesis, left parenthesis, x, plus, 6, right parenthesis
Line 3: =
(4x+9)(x+6)
Line 1 to Line 2:
Line 2 to Line 3:
Line 1: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 9, plus, 4, x, right parenthesis
Line 1: =
(x+6)(9+4x)
Line 2: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 4, x, plus, 9, right parenthesis
Line 2: =
(x+6)(4x+9)
Line 3: , left parenthesis, 4, x, plus, 9, right parenthesis, left parenthesis, x, plus, 6, right parenthesis
Line 3: =
(4x+9)(x+6)
Line 1 to Line 2:
Line 2 to Line 3:
Answers
GPT-4o mini
The properties that justify the steps are as follows:
Line 1 to Line 2: **Commutative Property of Addition**
This property states that the order in which numbers are added does not affect the sum. Here, the expression changes from \( (9 + 4x) \) to \( (4x + 9) \).
Line 2 to Line 3: **Commutative Property of Multiplication**
This property states that the order in which numbers are multiplied does not affect the product. In this case, the expression changes from \( (4x + 9)(x + 6) \) to \( (x + 6)(4x + 9) \).
Line 1 to Line 2: **Commutative Property of Addition**
This property states that the order in which numbers are added does not affect the sum. Here, the expression changes from \( (9 + 4x) \) to \( (4x + 9) \).
Line 2 to Line 3: **Commutative Property of Multiplication**
This property states that the order in which numbers are multiplied does not affect the product. In this case, the expression changes from \( (4x + 9)(x + 6) \) to \( (x + 6)(4x + 9) \).