You must:

Label and display your new polynomial identity
Prove that it is true through an algebraic proof, identifying each step
Demonstrate that your polynomial identity works on numerical relationships

Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity.

Column A Column B
(x − y) (x2 + 2xy + y2)
(x + y) (x2 − 2xy + y2)
(y + x) (ax + b)
(y − x) (cy + d)