Basic Concepts of Algebra

by Wonder Boy · Published July 26, 2019 · Updated April 15, 2020

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.

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.