Make a polynomial identity. Using the given equations, demonstrate the proof of polynomial identity through an algebraic proof and a numerical proof in an engaging way.

Label and display your new polynomial identity

Prove that it is true through an algebraic proof, identifying each step

(x - y)

(x + y)

(y + x)

(y - x)

(x + a)

(y + b)

(x2 + 2xy + y2)

(x2 - 2xy + y2)

(ax + b)

(cy + d)

Base on the question which ask to prove that the said expression is true through an algebraic proof and in my further research, the answer would be the following:

x (y + x) + y (y + x) distributive property

xy + x2 + y2 + xy distributive

x2 + xy + xy + y2 associative

I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarifications