When you have
(a+b)^2 you can change it into a^2+2ab+b^2
How does it work when I am increasing the exponent?
Like (a+b)^3,(a+b)^4..

Question

When you have
(a+b)^2 you can change it into a^2+2ab+b^2
How does it work when I am increasing the exponent?
Like (a+b)^3,(a+b)^4..

lyrae · Answer

http://en.wikipedia.org/wiki/Binomial_coefficient#Definition_and_interpretations

akashdeepdeb · Answer

Well, for $(a+b)^n$ expansion particularly, there is a thing called, Pascal's Triangle.
There is this thing known as Binomial theorem; we use it for the expansion. 

eg.

$$(a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2$$
$$(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$$

akashdeepdeb · Answer

Here is a pattern of their coefficients:

1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Can you guess the pattern? ;-)

anonymous · Answer

Yea, yea, I already heard about that. You know, I am 14 years old and I got really interested into math, I am starting with calculus. Done limits and I was doin functions like f(x)=x^2 so f'(x)=? [ I hope you know what i mean]. And I have seen that pattern like (a+b)^2 = a^2 + 2ab + b^2 so I got bit interested in.. I Will try to get what you said and read more about that. Thank you and have a nice day! :)

geerky42 · Answer

You may like to read this: http://www.mathsisfun.com/algebra/binomial-theorem.html

geerky42 · Answer

Also, this: http://wdjoyner.com/teach/calc1-sage/html/node106.html Similar pattern.

anonymous · Answer

I`m trying to understand this, too. So a new operation appears in every bigger power of (a+b). But I can`t find any pattern, how to generate this new opperation...