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)
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: $\displaystyle (a + b)^n = \sum_{k = 0}^n {n \choose k} a^kb^{n - k}$, you can switch a and b, and usually i prefer to do so, and write $\displaystyle \sum_{k = 0}^n {n \choose k}a^{n - k}b^k$
and by $\displaystyle {n \choose k}$ i mean $\displaystyle _nC_k = C_k^n = \frac {n!}{k!(n - k)!}$
So $\displaystyle (a + b)^4 = \sum_{k = 0}^4 {4 \choose k}a^{k}b^{n - k} = b^4 + 4ab^3 + 6a^2b^2 + 4a^3b + a^4$
can you continue?