What are Algebraic Expressions?

Think of algebraic expressions as mathematical phrases that mix numbers, letters, and operation signs (+, -, ×, ÷). Unlike equations, expressions don't have an equals sign - they're just a collection of mathematical terms waiting to be worked with.

The letters in expressions are called variables, and they represent unknown numbers. A term is each separate part of an expression, like 4x, -5y, or just 8 on its own.

Like terms are terms that have exactly the same variable part, including any powers. For example, 3x and -5x are like terms because they both have just 'x'. However, 3x and 3x² are NOT like terms because one has x and the other has x².

Remember: Expressions are the foundation for solving equations later, so getting comfortable with these basics now will make your life much easier!

Writing Expressions from Words

Converting word problems into algebraic expressions is all about spotting the right keywords. Once you know what to look for, it becomes like translating from English to maths.

Addition keywords: plus, sum, more than, increased by Subtraction keywords: minus, difference, less than, decreased by
Multiplication keywords: times, product, of (like "half of a number") Division keywords: divided by, quotient, shared between

Watch out for tricky phrases like "8 less than a number x" - this becomes x - 8, not 8 - x. The order matters! "A number n increased by 10" simply becomes n + 10, while "the product of 7 and a number y" becomes 7y (no multiplication sign needed).

Top tip: Always double-check the order, especially with subtraction. "Less than" flips the order around!

Simplifying by Collecting Like Terms

Simplifying expressions is like tidying your room - you group similar things together. You can only combine terms that are exactly the same type, just like you can add apples to apples but not apples to oranges.

Here's your step-by-step process: First, identify all the terms in the expression. Next, find groups of like terms - it helps to circle them in different colours. Remember to include the + or - sign with each term!

Then add or subtract the coefficients (the numbers in front) of like terms. Finally, write your simplified expression.

Let's try: 5x + 3y - 2x + 7y + 4. Group the x terms $5x and -2x$, the y terms (3y and 7y), and the constant (4). Combine: 5x - 2x = 3x, 3y + 7y = 10y, and 4 stays as is. Your answer: 3x + 10y + 4.

Watch out: The sign in front of a term belongs to that term! So -2x means negative 2x, not positive 2x that you subtract later.

Evaluating Expressions

Evaluating expressions means finding the actual number value when you're given specific values for the variables. It's like following a recipe when you finally know all the ingredients.

Your method is simple: write the expression, replace each variable with its given number (use brackets to avoid mistakes!), then use BIDMAS to calculate your final answer.

BIDMAS stands for: Brackets, Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right).

Example: Evaluate 4a - 2b when a = 5 and b = 3. Substitute: 4(5) - 2(3). Calculate: 20 - 6 = 14.

Pro tip: Always use brackets when substituting, especially with negative numbers. If x = -3, then x² = (-3)² = 9, not -3² = -9!

Key Points for Success

The most important thing to remember is that expressions have no equals sign, while equations do. Don't mix them up in exams!

When collecting like terms, that + or - sign stays with its term. You can't combine terms that aren't alike - 7x and 4y stay as 7x + 4y, and 2x and 3x² can't be combined either.

Always use brackets when substituting values, and never skip BIDMAS when evaluating. These simple rules will save you from most common mistakes.

Quick recap: Variables are letters for unknown numbers, terms are the separate parts of expressions, like terms have identical variable parts, simplifying means collecting like terms, and evaluating means substituting numbers and calculating.

Exam success: Master these basics now, and algebraic expressions will become your mathematical superpower for tackling more complex problems later!