# Thread: Hi, i need help to expand this binomial and write it simply

1. ## Hi, i need help to expand this binomial and write it simply

I need to expand this binomial fully and then write it as simply as possible thnx for help

(2+4)^4 (^ meaning to the power of)

2. Originally Posted by Chez_
I need to expand this binomial fully and then write it as simply as possible thnx for help

(2+4)^4 (^ meaning to the power of)
aren't you missing an x or something somewhere?

3. oh yes sorry mis wrote it,
should be (2+X)^4

4. Originally Posted by Chez_
oh yes sorry mis wrote it,
should be (2+X)^4
there are two main ways to expand a binomial. one is using Pascal's triangle. the other is using the binomial theorem. i assume you learned the latter, since it is the method more generally taught.

the binomial theorem basically says: $(a + b)^n = \sum_{k = 0}^n {n \choose k} a^kb^{n - k}$, you can switch a and b, and usually i prefer to do so, and write $\sum_{k = 0}^n {n \choose k}a^{n - k}b^k$

and by ${n \choose k}$ i mean $_nC_k = C_k^n = \frac {n!}{k!(n - k)!}$

So $(a + b)^4 = \sum_{k = 0}^4 {4 \choose k}a^{k}b^{n - k} = b^4 + 4ab^3 + 6a^2b^2 + 4a^3b + a^4$

can you continue?