Question

Which of the following demonstrates the Commutative Property of Multiplication?

3(4a − 2) = 12a − 6
3(4a − 2) = (4a − 2) ⋅ 3
12a − 6 = (4a − 2) ⋅ 3
(3 ⋅ 4a) − 2 = 3(4a − 2)

Answer 1

The answer is 3 (4a-2)=(4a-2)•3

Answer 2

`3 \cdot (4a - 2) = (4a - 2) \cdot 3`

Explanation:

Commutative property of multiplciation is

`a \cdot b = b \cdot a`

`3(4a - 2) = 12a - 6`

Here 3 is multiplied inside the parenthesis. Distributive property is applied.

`3 \cdot (4a - 2) = (4a - 2) \cdot 3` is same as
`a \cdot b = b \cdot a`

Here, the terms 3 and 4a-2 are interchanged. So this equation demonstrates the commutative property of multiplication.

`12a - 6 = (4a - 2) \cdot 3`

GCF 3 is factored out. factoring is applied.

`(3 \cdot 4a) - 2 = 3(4a - 2)`

Here 3 is not a common factor.