# 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.

# Inequality

**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.