Question

Can you please help me with some algebra? :) It's my 4.08 Polynomial Identities and Proofs assignment. Just an explanation, please!?

Answer 1

Make a polynomial identity. I have to demonstrate the proof of my 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)

Answer 2

This is what i have to do using the examples provided, but i don't know how. Please help?

Answer 3

Here's a polynomial identity you could make with those:
(x + y)(y + x) = (x2 + 2xy + y2)

Answer 4

Proof
(x + y)(y + x)
x(y + x) + y(y + x) distributive property
xy + x2 + y2 + xy distributive
x2 + xy + xy + y2 associative
x2 + 2xy + y2 not sure what exactly that property is called. sorry

Answer 5

For a numerical example, just plug in something for x and y and see if it works
Let x = 1 and y = 2
(1 + 2) * (2 + 1) = 3 * 3 = 9
1^2 + 2*1*2 + 2^2 = 1 + 4 + 4 = 9
9 = 9 check

Answer 6

Thank you so much! This was a lot of help! I will come back if i need anything else :) Thank you!!!