Term algebra is the most important semantics of theoretical data types, where this declaration provides the signature of a multi-sorted algebraic structure and algebra is an existing model of the theoretical declaration. Algebra is the term which plays a vital part in mathematics that uses mathematical statements to define relationships among things that vary over time. It includes real numbers, complex numbers, matrices, vectors etc. When we make use of a mathematical statement to define a relationship, we often use letters to denote the quantity that varies. The letters and symbols are denoted as variables. The terms in algebra includes Variables, Coefficients, Exponents, Constants, Equations, Expressions, Monomials, Binomials and Polynomials, Linear equations, quadratic equations and cubic equations. Let us make ourselves familiar to some of the important and basic terms used in algebra.
The following terms are mainly used in algebra are explained clearly with examples,
Variables
Coefficients
Exponents
Constants
Equations
Variables:
In algebra, the letter that stands for an unknown value is known as a variable. The variables in the term 10x^{3}y^{4} are x and y.
Coefficients:
The value that multiplies a variable or variables is known as the coefficient. It is generally written in front of the variable or variables. The coefficient in the term 10yz^{4} is 10. When the coefficient is 1, it is generally not written (i.e., 1yz^{3} = yz^{3} and 1a^{4} = a^{4}).
Exponents:
The power to which a variable is increased is known as the exponent. The exponent in 9a^{6} is 6. When the exponent is 1, it is generally not written (i.e., 9y^{4}z^{1} = 9y^{4}z). Any variable or value increased to the power zero gives one (i.e., a^{0} = 1).
Constants:
The value does not change or in other words "Fixed quantity".
For example: 3, 5,`pi`
Equations:
The equation in algebra consist of equal sign in which the value of both sides of the expression must be same.
For example: 6+5 = 10+1
Expressions:
The expression consists of variables, constants and symbols. It does not contain the equal sign.
For example: 3x+4, y+6, x+y+z
Quadratic equations:
The quadratic equation is a second degree equation. The general quadratic is of the form ax^{2}+bx+c, where a, b,c are constants and x is the variable.
For example:
3x^{2} + 2x +6, m^{2} - 3m + 5