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.