Question

Below is an Algebraic Proof that shows how the expression x(1+y) + y(2+x) is equivalent to x + 2xy + 2y. Some of the steps are labeled with the action or property. Match the following properties in the order they are used in the proof.

Answer 1

Explanation:

Steps Property

x(1 + y) + y(2 + x) Given

x + xy + 2y + xy Distributive property

x + xy + xy + 2y Commutative property of addition

[a + b = b + a]

x + (xy + xy) + 2y Associative property of addition

[(a + b) + c = a + (b + c)]

x + 2xy + 2y Combine like terms