Question

Are the expressions 4a+(5a+3c) and (4a+5a)+3c equivalent? If so, determine what property can be applied to determine that they are equivalent.

Answer 1

Yes, they are equivalent expressions, by the Associative Property

Explanation:

Both of these expressions are equal to:

4a + 5a + 3c

(and then, 9a + 3c)

This is all adding so you can add them all up without any of the parentheses. In the question at first the parentheses are grouping together the 5a and 3c, but in the second expression they are wrapped around the 4a and 5a. But in both expressions the order of the three terms does not change. Only the grouping changes. The terms are grouped differently, but the order DOES NOT change. This is Associative property. If the order changes it is Commutative property.