Add Maths>Binomial Expansion and Distribution
Binomial Expansion
For an equation such as the one below, you could expand it by writing it out as shown below and multiplying the bracket before collecting like terms but that would be timeconsuming, tedious and prone to errors. $$ (2x+3)^5 = (2x+3)(2x+3)(2x+3)(2x+3)(2x+3) $$
For this reason, when the powers (values of n) get higher, it makes more sense to use a form of shortcut.
For this reason, when the powers (values of n) get higher, it makes more sense to use a form of shortcut.
One such shortcut is to use Pascal's triangle (to the left) to work out the coefficients of each tern and then to use other trends to figure out the rest, as shown below. The trends are:

However, writing out Pascal's Triangle can be tedious and timeconsuming, especially when it get to higher powers. fortunately, there is a way to find out what these number are using a calculator function or a formula where n is the power of the expansion and r is the power of b.
The general formula for a binomial expansion is as follows for values of n that are integers (whole numbers) that are not negative:
Note how we have already used this formula but we're removing unnecessary details such as values which will always equal 1.
If asked to find the term of or coefficient of some power of x in a binomial expansion, instead of doing the entire expansion, we can use the trends to answer quickly: substitute a, b and n. Ensure the power of x is the power they ask for by making x raised to that power and then fill out the rest of the details, given that the powers must add to n. Here is an example (to the right):

Binomial Distribution
Binomials can also be used for working out probabilities. (If you need a refresher, the probability rules are at the top of the page)
Additionally (though this can be determined with the above rules), if A and B are mutually exclusive, P(A or B) = P(A) + P(B).
In a scenario where...
Additionally (though this can be determined with the above rules), if A and B are mutually exclusive, P(A or B) = P(A) + P(B).
In a scenario where...
 there are n independent trials (which each have the same probabilities of 'success'  the outcome we're searching for the probability of)
 The outcomes are p (success) and p (failure) and are mutually exclusive (if one happens, the other doesn't)
 The number of successes is X
Example Question
If I role a fair 6sided die 11 times, what is the probability that I get one of a 4 or a 5 6 times
If I role a fair 6sided die 11 times, what is the probability that I get one of a 4 or a 5 6 times
note  It is worth noting that the probabilities X=0, X=1, X=2... are the respective terms in the expansion of $$ (p+q)^n $$