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Polynomial Identities and Proofs
Transcript of Polynomial Identities and Proofs
Numerical Expression or Example
(x – y)
(x + y)
(y + x)
(y – x)
(x + a)
(y + b)
(x2 + 2xy + y2)
(x2 – 2xy + y2)
(ax + b)
(cy + d)
The polynomial identity made from the original polynomial
Here is the proof
The Polynomial Identity
(x + y)(y + x) = (x2 + 2xy + y2)
(x + y)(y + x)
x(y + x) + y(y + x) - known as distributive property
xy + x2 + y2 + xy - known as distributive property
x2 + xy + xy + y2 - known as associative property
x2 + 2xy + y2 - known as communitive property
If you are going to use a numerical example or expression then you will need to plug in something for x and y and see if it works
If you 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 then check it