When it comes to studying Algebra, there are several basic mathematical terms that you will go through.

Before we move into the detailed study of Algebra, it’s good to familiarize yourself with a few basic Algebraic terms.

An equation can be defined as a statement involving symbols (variables), numbers (constants) and
mathematical operators (Addition, Subtraction, Multiplication, Division etc) that asserts the
equality of two mathematical expressions. The equality of the two expressions is shown by using
a symbol “=” read as “**is equal to**”. For example: 3X + 7 = 16 is an equation in
the variable X.

A variable is a symbol that represents a quantity in an algebraic expression. It is a value
that may change with time and scope of the concerned problem. For example: in the equation 3X +
7 = 16, X is the variable. Also in the polynomial X^{2} + 5XY – 3Y^{2}, both X and Y are
variables.

An equation that involves only one variable is knows as a One Variable Equation.

3X + 7 = 16
is an example of it.

An equation that involves two variables is knows as a Two Variable Equation. 2X + Y = 10 is
a Two Variable Equation of where X and Y are variables. Please note that here both X and Y have a power or exponent of 1.
Hence it is an equation with degree 1. The degree is equal to the highest power of the variable(s) invloved. X^{2} +
5XY – 3Y^{2} = 25 is an example of a Two Variable Equation of degree 2.

An equation that comprises three variables / symbols is called a Three Variable Equation

x + y − Z = 1 -------------(1)

8x + 3y − 6z = 1 -------------(2)

−4x − y + 3z = 1 -------------(3)

The above three equations form a system of 3 equations in 3 variables X, Y and Z. Each of
these equations is a Three Variable Equation of degree 1. Also these equations are called ** Linear equations** in three variables.

A monomial is a product of powers of variables. A monomial in a single variable is of the
form **x**^{n} where X is a variable and n is a positive integer. There can also be
monomials in more than one variable. For example **x**^{m} **y**^{n} is a
monomial in two variables where m,n are any positive integers. Monomials can also be multiplied
by nonzero constant values. 24x^{2} y^{5} z^{3} is a monomial in three variables x,y,z with exponents 2,5 and 3 respectively.

A polynomial is formed by a finite set of monomials that relate with each other through the
operators of addition and subtraction. The order of the polynomial is defined as the order of
the highest degree monomial present in the mathematical statement. 2x^{3} + 4x^{2} + 3x – 7 is a polynomial of order 3 in a single variable.

Polynomials also exist in multiple variables. x^{3} + 4x^{2}y + xy^{5} + y^{2} – 2 is a polynomial in variables x and y.

Exponentiation is a mathematical operation written as **a ^{n}** where a is the base
and n is called

Shown below is a graph that shows exponentiation for different values of bases a.

By looking at the graph we conclude that the numbers less than one approach to zero as the exponent value grows. On the other hand, the exponentiation values tend to infinity as exponentiation index grows for numbers greater than 1.

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