Math Lesson 4:
Algebra

4.1 Algebraic Expressions

Welcome to the exciting world of algebra! In this section, we'll introduce you to the building blocks of algebraic expressions: variables and constants.

A variable is a symbol (usually a letter) that represents an unknown value. For example, 'x' could represent any number.

A constant is a fixed value that doesn't change. For example, 5 is a constant.

An algebraic expression is a combination of variables, constants, and mathematical operations (+, -, ×, ÷).

Example: 3x + 2 is an algebraic expression where 'x' is a variable and 3 and 2 are constants.

4.2 Addition and Subtraction

Adding and subtracting algebraic expressions is just like adding and subtracting numbers, but we have to pay attention to the variables.

Rule: We can only combine terms with the same variable and exponent.

Example: 2x + 3x = 5x, but 2x + 3y cannot be simplified.

4.3 Multiplication and Division

Multiplying and dividing algebraic expressions involves applying the rules of exponents and distributing.

Rule: When multiplying terms with the same variable, we add their exponents.

Example: x^2 * x^3 = x^(2+3) = x^5

Rule: When dividing terms with the same variable, we subtract their exponents.

Example: x^5 / x^2 = x^(5-2) = x^3

4.4 Factorising

Factorising is the process of breaking down an expression into a product of its factors. It's the reverse of expanding.

Common factor: When all terms share a common factor, we can factor it out.

Example: 2x + 4 = 2(x + 2)

Difference of squares: a^2 - b^2 can be factored as (a+b)(a-b)

Example: x^2 - 9 = (x+3)(x-3)