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# 04.08 Polynomial Identities and Proofs

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## Joanna Torres

on 10 February 2014

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#### Transcript of 04.08 Polynomial Identities and Proofs

04.08 Polynomial Identities and Proofs
Numerical Proof
To prove that it reall does work, we're going to throw some numbers in! lets do x=7 y=8
First plug it in
(x+y)(x+y)(x+y)=x^3+3x^2y+3xy^2+y^3
(7+8)(7+8)(7+8)=(7)^3+3(7)^2(8)+3(7)(8)^2+(8)^3
(15)(15)(15)=343+416+1344+512
3375=343+1176+1344+512
3375=3375

Algebraic Proof
Lets begin by solving the side that is not simplified!
(x+y)(x+y)(x+y)

Use the distributive property

(x+y)(x+y)(x+y)=x^3+3x^2y+3xy^2+y^3

=x^3+3x^2y=3xy^2+y^3

Easy, right?
End
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