Final answer:
The binomial expansion formula in the binomial theorem includes variables such as the bases a and b, the exponent n, the binomial coefficient C(n, k), and the probabilities of success (p) and failure (q) to express (a+b)^n as a series.
Step-by-step explanation:
The variables that make up the binomial expansion formula in the binomial theorem are:
- a: one base of the binomial (a+b)^n
- b: the other base of the binomial (a+b)^n
- n: the exponent to which the binomial is raised
- C(n, k) or (n choose k): the binomial coefficient, which is the number of ways to choose k successes in n trials
- p: the probability of success in each trial
- q: the probability of failure in each trial (q=1-p)
The binomial expansion allows us to write (a+b)^n as a sum of terms of the form C(n, k)a^(n-k)b^k, where k is the term in the series. Each term in the expansion represents a possible result of n independent trials, each of which can result in a success (with probability p) or failure (with probability q), which is a reflection of the binomial distribution.