The Associative Property of Multiplication justifies rearranging factors within parentheses, as shown in the transition from Line 1 to Line 2 and Line 2 to Line 3.
In the provided expressions c(bd), (cb)d, and (bc)d, the property being applied is the Associative Property of Multiplication. This property asserts that the product of three or more numbers remains the same regardless of how the numbers are grouped. Mathematically, it is represented as (a * b) * c = a * (b * c).
Line 1: c(bd) signifies the multiplication of c by the product bd. This step is justified by the Associative Property, as it doesn't matter if we first multiply b and d and then multiply the result by c, or if we first multiply c and b and then multiply the result by d.
Line 2: (cb)d is derived by rearranging the terms within the parentheses, applying the Associative Property. It illustrates that whether we multiply c and b first and then multiply the result by d, or if we first multiply b and d and then multiply the result by c, the final product remains the same.
Line 3: (bc)d is another rearrangement of the terms within the parentheses, maintaining the same product. This step is also justified by the Associative Property.
In summary, the application of the Associative Property of Multiplication allows us to rearrange the grouping of factors without changing the result of the multiplication.
The question probable may be:
Identify the property that justifies each step asked about in the answer area below.
Line 1 : c(bd)
line 2 : (cb)d
line 3: (bc)d
Line 1 to line 2:
Line 2 to line 3: