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How do you expand algebraic expressions to the nth power?

  • Thread starter WilliamK
  • Start date
  • #1
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I would like to start by saying that I'm not at school, I'm 40 years old, and learning calculus for the first time - personal, private study - so anyone helping me out won't be giving me the answers to any course work or school work. I don't have a teacher, and there's no one I can ask who can help me, so I've come to this forum hoping some kind soul can help me.

Homework Statement



I'm trying to understand how to differentiate y=x^n, but I get stuck at the expansion stage

Homework Equations



In all cases, we are increasing y by a small amount (dy)

Example 1:
y+dy = (x+dx)^2
expanded out, it becomes: y+dy = x^2 + 2x.dx+(dx)2

Example 2:
y+dy = (x+dx)^3
expanded out, it becomes y+dy = x^3 + 3x^2.dx+3x(dx)^2+(dx)^3

Final Example:
y+dy = (x+dx)^4
expanded out, it becomes y+dy = x^4 + 4x^3dx+6x^2(dx)^2 + 4x(dx)^3 + (dx)^4

My calculus textbook assumes a knowledge I don't have.

Can someone please explain clearly & simply how one is supposed to derive these expanded expressions? Or even refer me to an external link which explains it?

Many thanks
 
Last edited:

Answers and Replies

  • #2
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Wikipedia explains it nicely. http://en.wikipedia.org/wiki/Binomial_theorem" [Broken] If you don't understand something there, feel free to ask.
 
Last edited by a moderator:
  • #3
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Thanks for the link, Sourabh, I'll take a look. (Its been 25 years since I last did algebra, and I'm not even sure if I covered binominal theorum at school, lol)
 

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