To provide you with a clearer understanding, let's analyze the structure of what you're asking and identify the correct properties that justify the steps from line to line. Given the context, it seems you are representing certain steps in an algebraic manipulation involving variables and possibly coefficients.
Line 1 to Line 2:
Line 1: a(sd)
Line 2: (as)d
Justification: Associative Property of Multiplication
The associative property allows you to group factors in different ways. In this case, you can change the grouping of factors from a(sd) to (as)d.
Line 2 to Line 3:
Line 2: (as)d
Line 3: (sa)d
Justification: Commutative Property of Multiplication
The commutative property states that the order in which you multiply numbers does not change the product. Hence, (as)d can be regrouped or rearranged to (sa)d.
Summary of Justifications:
- From Line 1 to Line 2: Associative Property of Multiplication.
- From Line 2 to Line 3: Commutative Property of Multiplication.
I hope this clarifies the properties used in each step! If you have any further questions or need additional clarifications, feel free to ask!