A bbinomial/b has the form ((a+b)n). When (n) is a bpositive integer/b, it can be expanded according to this formula:
((a+b)n = \dbinom{n}{0} a^n b^0 + \dbinom{n}{1} a^{n-1} b^1 + \dbinom{n}{2} a^{n-2} b^2 + ... + \dbinom{n}{n-1} a^1 b^{n-1} + \dbinom{n}{n} a^n b^0)
[b]uPascal's Triangle[/u]/b
The coefficients of the binomial expansion form a pattern known as Pascal's Triangle. (The first row is the 0th row.)
mtaimg/images/topics/4/4-32-1.png/mtaimg
For example, the 4th row of the triangle shows the coefficients for the expansion of ((a+b)4).
For high powers of (n), it is quicker to use the (nCr) method for finding the coefficients, because it takes a while to write out Pascal's Triangle.
[b]uUses of the binomial expansion[/u]/b
The binomial expansion can be used for approximations and calculating binomial probabilities.
[b]uBinomial expansion[/u]/b
((a+b)n = \dbinom{n}{0} a^n b^0 + \dbinom{n}{1} a^{n-1} b^1 + \dbinom{n}{2} a^{n-2} b^2 + ... + \dbinom{n}{n-1} a^1 b^{n-1} + \dbinom{n}{n} a^n b^0)