Binomial

An algebraic expression that contains two non-zero terms is known as a binomial. It is expressed in the form ax^m + bxⁿ where a and b number, x is variable, m and n are nonnegative distinct integers.

Examples:

• g + 3m is a binomial in two variables g and m.
• 3a⁴ – 5b²  is a binomial in two variables a and b.
• -4x² – 9y is a binomial in two variables x and y.
• a²/4 + b/2 is a binomial in two variables a and b.

Binomial Equation

Any equation that contains one or more binomials is known as a binomial equation.

Example:

v = u + 1/2 at²

Operations on Binomials

A few basic operations on binomials are 

• Factorization
• Addition
• Subtraction
• Multiplication
• Raising to the nth power
• Converting to lower-order binomials

Factorization:

A binomial can be expressed as the product of the other two.

Example: 

a² – b² can be expressed as (a + b) (a – b).

Addition:

Two binomials can be added if both contain the same variable and the same exponent.

Example:

(2a² + 3b) + (4a² + 5b) = 6a² + 8b

Subtraction: 

It is similar to addition, two binomials should contain the same variable and exponent.

Example:

(6a² + 3b) – (2a² + 5b) = 4a² – 2b

Multiplication:

When we multiply two binomials distributive property is used and it ends up with four terms. In this method, multiplication is carried by multiplying each term of the first factor to the second factor.

Example:

(ax + b) (mx + n) can be expressed as amx² + (an + mb) x + bn

Raising to nth Power: 

A binomial can be raised to the nth power and expressed in the form of  (x + y)ⁿ

Converting to Lower order binomials:

Higher-order binomials can be factored to lower-order binomials such as cubes can be factored to products of squares and another monomial.

Example:

a³ + b³ can be expressed as (a + b) (a² – ab + b²).

Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2nd degree), and cubic polynomial (3rd degree).

There are 3 types of polynomials based on the number of terms in the polynomial – monomial, binomial, and trinomial, and for more than that we use the general term polynomial. This article is about the types of polynomials – Monomials, Binomials, and Polynomials in detail.