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.

Step-by-step 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

f

step-by-step explanation:

f