# Playing with equations and functions [closed]

I have a weak math foundation. I decided to start all over again, beginning at algebra. I am looking for something specific but I am not sure how it is called.

Our math professor always plays with equations and functions. He constantly simplifies equations or functions by rewriting them. But sometimes I have no clue what is going on. I hope you know what I mean by that.

Do you know if there is a cheatsheet that contains all rules that I can use to simplify or transform an expression, equation or function?

Edit:

For example something like $x^2 + 1x -6 = (x - 2)(x + 3)$

Or if you do a derivation of sin, then you get cos.

So that I have all rules at one place.

Even something basic like $sqrt(4) = 2$ , $4 = 2^2$

edit2:

Found something useful http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet.pdf

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Can you provide some examples from your notes so we can provide better guidance? –  Amzoti Dec 30 '12 at 3:01
I would recommend some of the online video refresher courses. For example UCCS - Calculus Refresher Course. You can find Open Courseware examples and you might want to check out Khan Academy. Regards –  Amzoti Dec 30 '12 at 3:22
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## closed as not a real question by Jasper Loy, Ittay Weiss, Alexander Gruber♦, froggie, MicahDec 30 '12 at 6:49

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## 2 Answers

There isn't a cheatsheet. Part of mathematics is being familiar with various transformations and identities that are used. This is experience that you gain over time. You build up your interpretations of mathematical identities in your mind, through your understanding of them.

It will be helpful for you to start out with various factorizations. Try to factorize the following identities:

$x^2 - y^2$ (this should be familiar)

$x^n-y^n$, where $n$ is a natural number (this might be familiar)

$x^3+y^3+z^3 - 3xyz$ (this will likely be new)

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what is the third one? –  Omnitic Dec 30 '12 at 3:30
$(x+y+z)(x^2 + y^2 + z^2 - xy -yz- zx)$ - Related to $(a+b)^3 = a^3 + b^3 + 3ab(a+b)$. Can be used to show the 3-varibale AM-GM directly. –  Calvin Lin Dec 30 '12 at 3:34
@Khromonkey Don't know how to send messages on this. I'm in the chat room now, and saw your messages in the past hour. –  Calvin Lin Dec 30 '12 at 4:06
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First up. If you do equal things to equal things you get equal things: examples

$2x=1 \rightarrow x=\frac{1}{2}$ or $x+1=2 \rightarrow x=1$

In the first one we divided both things by 2 in the second example we subtracted 1 from both sides

second in the list: factorizing

$(a+b)^2=a^2+2ab+b^2$ (perfect square)

$1+2+3+4+5...+n= \frac{n(1+n)}{2}$ (sum of first n positive integers)

Gaussian summation: the sum of an arithmetic sequence is always $\frac{(f+l)(t)}{2}$ where f is the first term,l the last and t the number of terms

$1+x+x^2+x^3+x^4+...+x^n=\frac{x^{(n+1)}-1}{x-1}$ Sum of geometric series

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The sum of first $n$ integers you give cannot be right, first of all your formula suggests that it can be non-integer, secondly if $n>2$, we have that $n>1+n/2$ and the sum can only be bigger. I suppose you meant $\frac{n(n+1)}{2}$ for this sum. In this I have assumed as well that you meant the first $n$ positive integers. –  user50407 Dec 30 '12 at 4:19
Mr.FS you are 100% right, sorry for the mistake. I will fix it now. Thanks for pointing it out, please take the liberty to correct future posts by me when they are so obviously wrong. –  Omnitic Dec 30 '12 at 4:24
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