'dummy' variable - algebra

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Main Question or Discussion Point

Does anyone know any good websites or information on dummy variables in algebra.

Let me explain what i mean by dummy variable, what i mean is a pro-numeral that one inserts into an algebraic expression such that the expression stays the same but such that you can factorize it neatly. For example if i have x2 + 6x. If i add a dummy variable, it might factorize more elegantly. I decide to use 9

x2 + 6x + 9 - 9

I have to minus the nine as well to keep the original expression the same. I shall factorize the first 3 terms, it becomes

(x + 3)2 - 9

9 is 32

(x + 3)2 - 32

Using the difference of 2 squares

(x + 3 - 3)(x + 3 + 3) = x(x + 6)

So this is the long way, but some times you cant factorize an expression and using a dummy variable helps. You cant factorize a4 + 4b4 with out a dummy variable

So back to my question, does any one know of any webs sites or stuff that has more info or exercises on dummy variables in algebra?
 

Answers and Replies

CompuChip
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I wouldn't call it "inserting a dummy variable", in fact I wouldn't call 9 a variable at all. It's more like: "find a clever way to add 0", by adding + c - c to the expression for some well-chosen c.
One particular recipe is called "completing the square" which is basically what you are using in your example. In general, which term one would add (and subtract) would depend on the problem.

(By the way, [itex]x^2 + 6 x[/itex] factors immediately by taking out x).
 
symbolipoint
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kurt.physics, in your last step, you accomplished the reverse of completing the square.

A dummy variable is just a variable which fits in a form of expression. You would see "dummy variables" used often in Calculus. You may need to infer the meaning at that time. [my somewhat limited viewpoint]

This link may also help: http://documents.wolfram.com/v4/MainBook/2.6.5.html [Broken]

Also be aware that the term "dummy variable" is used in 'regression analysis'.
 
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Gib Z
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In both your examples you are completing the square.
 

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