Elementary algebra is the study of the arithmetic operators (+, -, *, /)
and their rules along with the combinations of algebraic variables. If
we combine some constants with some unknown variable, together with some
arithmetic operations, then the expression is termed as an algebraic
equation. The following are some of equations, representing algebraic
equations or algebraic expressions.
Consider the following algebraic expression:
In the above mentioned algebraic expression or polynomials, 5x², 2y, 9xy, and 4 are known as terms.
Consider the term 9xy, here xy is the variable and the coefficient is 9. Similarly, in the term 2y, 2 is the coefficient and y is the variable.
There can be 3 types of algebraic expressions. A monomial that contains only one term, a binomial expression that contains two unlike terms and a trinomial that contains exactly three unlike terms. By looking at the above mentioned figure of algebraic expression we can clearly differentiate between these.
Elementary algebra includes many topics, out of which the most commonly used are mentioned below:
- Factorization of ax2 + bx + c = 0 (Quadratic equations) over the set of integers.
- Operations with the algebraic fractions involving addition, subtraction, multiplication, and division.
- Division of monomials and other polynomials including the simplification of algebraic fractions.
- Solution to the linear equations and inequalities.
- Solving the simultaneous system of linear equations.
- Quadratic equations solution by the method of factoring.
- The conversion of written phrases or sentences into algebraic expressions or equations.
- Solving any verbal problem in an algebraic way including its geometrical reasoning through graphing.