#### Answer

a) distributive property
b) associative property of addition

#### Work Step by Step

a) This is an example of using the distributive property. The distributive property can be used to simplify a multiplication problem when one of the factors is a sum. The other factor is multiplied by each of the addends, and those products are then summed. In this example, the sum is "b+c" and the other factor is a. a is multiplied by b and by c, and those products are summed.
b) This is an example of using the associative property. The associative property says the grouping of addends does not change the sum. In the first expression, "a+b" is simplified first. In the second expression, "b+c" is simplified first. The associative property tells is these two expressions are equivalent.