A binomial can be viewed as an algebraic expression denoting the sum of two unlike terms. Examples of binomials are x + y, 3a -2b, x2 + y2 and so on. When the powers of binomials are expanded, the resulting polynomials display certain pattern. Binomial theorem summarizes the pattern in binomial expansions.

Binomial expansions and coefficients finds application in many other mathematical studies like binomial probabilities. Even though the general binomial expansion is intimidating in the first look, once the pattern is recognized, it is a very interesting mathematical concept to work with.

Binomial expansions are the polynomials resulting from expanding powers of binomials. The binomials are expanded by repeatedly multiplying the binomials as required.

The binomial expansions for powers 0 to 5 are given below:

Binomials

Pascal's triangle is the pattern got by picking the coefficients from successive binomial expansions and arranging them in the same order.

Pascal Binomial Expansion

The following pattern can be observed from Pascal's triangle. A number in a row is got by adding the two consecutive numbers in the row above.