# Basic Concepts of Algebra

The **Variables** and **constant coefficients** combine to form **algebraic terms** and these algebraic terms combine to form **Algebraic expressions**. To combine the algebraic expressions **mathematical operators** are used.

**Quotlly**

Example of variable : x,y,z

Example of Constant Coefficient: 1,4,9,34

Example of algebraic term: x^2 , 4xy, y^2, 3x^2y

In an algebraic term 3x^2y, 3 is constant coefficient and x^2y is variable.

**Like Terms **

Those algebraic terms in which power of variables are same are like terms.

E.g. 6x^3y and 10x^3y are like terms.

3xy^2 and 5xy^2 are like terms.

**Monomial **

If an algebraic expression contain only one term, then it is called a **Monomial .**

E.g. 2xy,

5x^2y,

10xyz

45

**Binomial**

If an algebraic expression contains two terms, then it is called a **Binomial.**

E.g. x + y,

x + 3y,

x+3y^2

xy + 3xy^2

**Trinomial**

If an algebraic expression contains three terms, then it is called a **Trinomial.**

E.g. x + y + z,

x + 3y + 5z,

x+ 3y^2 + 5z^5

xy + 3xy^2 +5xy^7

**Polynomial**

If an algebraic expression contains two or more terms, then it is called a **Polynomial.**

E.g. x + y

x + 3y + 5z,

x+ 3y^2 + 5z^5

**Polynomial in One Variable **

If an algebraic expression contains only one variable, then it is called a **Polynomial in one Variable.**

E.g. x + 3x^2

x + 3x^2 + 5x^3,

2x+ 3x^2 + 5x^5 +7x^6

**Degree of a Polynomial **

The greatest power of the variable in various terms is called **Degree of a polynomial.**

3x + 5x^2 + 7x^5 is a polynomial of degree 5.