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# C4 Binomial Expansion watch

1. Im currently studying C2 binomial expansion but I missed the lesson on it. Apparently we're using the C4 method to solve it, so not nCr and not . I asked my friend for the equation but I can't make heads or tails of it. If anyone can write this out in latex or something and explain it a bit that would be good, thanks.

(1+x)^n=1+nx+n(n-1)x^2/2! + n(n-1)(n-2)x^3/3!+...etc etc
2. All three methods give the same answers.

nCr (read n choose r) is defined as n!/(r!(n-r)!)

The coefficients of x^r in the binomial expansion of (1+x)^n are nCr

For example: nC3 = n!/((3!)(n-3)!)

Now n!/(n-3)! just cancels down to leave n(n-1)(n-2) and you've still got a 3! in the denominator
3. You have missed the point. You will not really need the formula for (1+x)^n for C2 stuff.

In C2, you will learn how to expand (a+b)^n. You will have been shown Pascal's triangle, and the nCr thingy.
The expansion is: a^n + nC1a^(n-1)b + nc2a^(n-2)b^2 + ... + nCra^(n-r)b^r
I think anyway. I'll admit I've never before used nCr notation. I liked Pascal's traingle.
But to be fair, binomial expansion was in C1 for me, so no calculator. Maybe if it's on C2 for you, n will be a large number that would make it impractical to use the triangle.

Anyway, on the questions with stuff like (1 + 2x)^4, you just rewrite a = 1, b = 2x, for your expansion of (a+b)^4. Remember that when you have b^3, it's (2x)^3 = 8x^3, not 2x^3.

For questions that ask for the coefficient of x^k for, say, (1 + 2x)^4 again, and you haven't already written out the expansion, then you need to notice that the coefficient of x^k is (nCk)(2^k)(1^(n-k)). If you don't understand this, quote me again.

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Updated: February 7, 2010
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