What is a binomial?

Binomials are used in algebra. They can be defined as:

An algebraic expression of the sum or the difference of two terms.

Or

Two polynomials (specifically monomials) connected by a plus or minus sign.

*Mono is Greek for one and Bi is Latin for two.

*A term is a combination of numbers and variables.

*If the terms are the same, they must have different exponents.

Monomial Example: 4x

Binomial Example: 4x+3

Typical Binomial Set-up: (a+b)^n

*a and b are the two terms.

Note: Exponenets cannot be negative or fractions and the denominator cannot contain variables.

Binomial Expansion, also commonly known as Binomial Theorem, is the expansion of any power (a + b)^n of a binomial (a + b) as a certain sum of products.

Example:

(a+b)^5 = (a+b)(a+b)(a+b)(a+b)(a+b)

(a+b)^5 = a^5+a^4b+a^3b^2+a^2b^3+ab^4+b^5

Use Pascal's triangle to fill in the coefficients.

Example: (x+y)^5 =

1x^5+5X^4y+10x^3y^2+10x^2y^3+5xy^4+1y^5

*Coefficients are the numbers in front of each term. Ex: 3x^2

3 is the coefficient