To justify each step, we will use properties of multiplication in algebra, specifically focusing on the associative property of multiplication. Here’s the breakdown of each line:
-
Line 1: c(bd)
- This is the starting point and doesn't require justification. It's simply a product of c and the product of b and d.
-
Line 2: (cb)d
- This step uses the Associative Property of Multiplication, which states that you can regroup the factors in a multiplication without changing the result. Specifically, the property allows us to move parentheses around. Thus, c(bd) can be rearranged to (cb)d.
-
Line 3: (bc)d
- This step also uses the Commutative Property of Multiplication, which states that the order of multiplication does not matter. In this step, we switch the order of the factors in the product "cb" to "bc", resulting in (bc)d.
In summary:
- Line 2 justifies using the Associative Property of Multiplication.
- Line 3 justifies using the Commutative Property of Multiplication.