2 (a + 3) = 2a + 6; Associative Property

Answer 1

The statement 2(a + 3) = 2a + 6 is an example of the distributive property, not the associative property.

The distributive property states that when you multiply a number by a sum, you can distribute the multiplication to each term within the sum.

In this case, you are multiplying 2 by the sum (a + 3), so you can distribute the 2 to both terms within the parentheses:
2(a + 3) = 2 * a + 2 * 3
= 2a + 6

The associative property, on the other hand, states that the grouping of numbers does not affect the result of addition or multiplication.

For example, the associative property of addition states that (a + b) + c = a + (b + c), meaning you can add numbers in any grouping and still get the same result.

However, the equation 2(a + 3) = 2a + 6 does not involve any addition or multiplication that would demonstrate the associative property.