The Basic Processes of Algebra

The Basic Processes of Algebra

Basic Definitions and Terminology

  • Algebra is a branch of mathematics where letters and symbols are used to represent numbers and quantities in equations and formulas.
  • An equation is a statement that two expressions are equal (e.g., 2x = 6). It expresses a fact or a principle.
  • A variable represents an unknown number or value. In algebra, variables are often represented by letters (e.g., x, y, z).
  • Constants are numbers that do not change their value.
  • Expressions are combinations of variables, numbers, and operations. They do not contain an equals (=) sign.
  • Coefficients are the numeric factors of variables (e.g., in 5x^2, 5 is the coefficient).

Algebraic Operations

  • Adding and subtracting like terms: When adding or subtracting algebraic expressions, you can only combine like terms. Like terms are terms that have the same variables raised to the same power.
  • Multiplication: Multiplication in algebra works under the same principle as in arithmetic. However, with algebra, you deal with variables in addition to numbers.
  • Division: Division is the operation that is the least commonly used with algebraic expressions. Division of algebraic expressions often involves the use of fractions.

Solving Simple Equations

  • Balancing the equation: To solve an equation means to find the value of the variable that makes the equation true. This is done by maintaining equality on both sides while simplifying the equation.
  • Use of inverse operations: An inverse operation undoes what the original operation does (addition-subtraction, multiplication-division).
  • Checking the solution: After finding a solution to an equation, always replace the variable in the original equation with the found value to confirm the solution.

Expanding and Factorising Algebraic Expressions

  • Expanding algebraic expressions: This refers to removing parentheses from equations by multiplying out.
  • Factorising algebraic expressions: Factorising is the reverse process of expanding. It involves expressing the expression as a product of factors.

Quadratic Equations

  • Quadratic equations have the form axe^2 + bx + c = 0. They are solved by factoring, completing the square, using the quadratic formula, or graphically.
  • Roots of a quadratic equation: The roots of a quadratic equation are the solutions to the equation. These are the values of x that make the equation true.


  • Inequalities: Instead of an equals sign, inequalities have less than, greater than, less than or equal to, or greater than or equal to signs.
  • Solving inequalities: Inequalities are solved in almost the same way as equations, with one key difference. When multiplying or dividing both sides by a negative value, the inequality sign flips (e.g., if a > b, then -a < -b).

All the aforementioned points provide a foundation for Further Mathematics. Ensure you understand these basics to be successful in the more advanced topics.