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# Polynomial Identities

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## Amber Carter

on 19 June 2014

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#### Transcript of Polynomial Identities

The New Identity
Algebraic Proof
Numerical Proof
The following is an advertisement for the newest polynomial identity. If you like the way your life is now and do not wish to add this new identity to your knowledge, then please do not go any further. This identity is not for those who are non-accepting of new and improved ideas.
Assignment details:
It's time to show off your creativity and marketing skills!
You are going to design an advertisement for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!
You may do this by making a flier, a newspaper or magazine advertisement, making an infomercial video or audio recording, or designing a visual presentation for investors through a flowchart or PowerPoint.
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
WARNING! No identities used in the lesson may be submitted. Create your own. See what happens when different binomials or trinomials are combined. Below is a list of some sample factors you may use to help develop your own identity.
• (x – y)
• (x + y)
• (y + x)
• (y – x)
• (x + a)
• (y + b)
• (x2 + 2xy + y2)
• (x2 – 2xy + y2)
• (ax + b)
• (cy + d)

(ax+b) (x+a)=ax^2 +a^2x +bx +ab

This identity is effective and easy to use!
To solve this you have to use the distributive property, more specifically FOIL
I hope this was adequate proof to convince you to love my new polynomial proof!
So, you want even more proof? Well then lets just substitute in values for a, b, and x. Lets make a=2, b=4, and x=6.

(ax+b) (x+a) = ax^2 +a^2x +bx +ab

Module 4.08
Amber Carter
Polynomial Identities
(ax+b) (x+a)
Use FOIL on first term
ax^2+a^2x
Use FOIL on second term
(ax+b) (x+a)
+bx +ab
ax^2+a^2x+bx+ab
((2*6)+4) (6+2) = (2^2*6) +(4^2*6) +(2*4)
(16) (8) = (24)+(96)+(8)
128 = 128
The numerical proof is correct! This identity had been proven right in front of your eyes
Full transcript