# Algebraic Language

**Algebraic Language**

**Basic Terminology**

**Constants**: Fixed values that do not change, such as 5, -3, or π.**Variables**: Letters used to represent numbers, such as x, y, or z.**Coefficients**: Numbers multiplying variables, such as the 3 in 3x.**Expressions**: Combinations of constants, variables, coefficients, and operations, such as 3x - 2.

**Operations**

**Addition (+) and Subtraction (-)**: Combine or remove quantities. For example, x + 2 or 5 - x.**Multiplication (x) and Division (÷)**: Increase or reduce quantities. For example, 2x or x ÷ 3.**Exponentiation (^)**: Raise a number to a power. For example, x^2 or 2^x.**Root (√)**: Extract the root of a number. For example, √x or 4√x.

**Algebraic Terms and Statements**

**Term**: A single part of an algebraic expression, separated by plus or minus signs. For example, in the expression 3x + 2y - 7, the terms are 3x, 2y and -7.**Equation**: A mathematical statement that establishes the equality of two expressions. For example, 3x - 2 = 4.**Identity**: An equation that is true for all possible values of the variable. For example, (a + b)^2 = a^2 + 2ab + b^2.**Inequality**: A statement that one expression may be greater than (<), less than (>), or not equal to (≠) another. For example, x > 3.**Function**: An expression that produces a single output (y) for every input (x). For example, y = 2x + 3.

**Manipulating and Simplifying Expressions**

**Like Terms**: Terms that contain the same variables raised to the same power. Like terms can be added or subtracted. For example, in 4x + 3x, the like terms are 4x and 3x.**Solving Equations**: The process of finding the values of the variable that make the equation true. Utilise the properties of equality.**Factoring**: The process of writing an expression as the product of its factors. For example, 3x^2 - 12x = 3x(x - 4).**Expanding**: Apply the distributive law to remove parentheses. For example, 2(x + 3) = 2x + 6.

**Useful Techniques**

**Substitution**: Replace variables with known or given values to solve equations or evaluate expressions.**Rearranging Equations**: Manipulate equations to isolate desired variables, often using operations in reverse.**Completing the Square**: A technique used to solve quadratic equations, write equations in vertex form, or graph parabolas.**Quadratic Formula**: A method to solve any quadratic equation, found by completing the square on ax^2 + bx + c = 0.