Simplifying Algebraic Expressions

This lesson explains simplifying algebraic expressions step by step using clear GCSE examples.

What are algebraic expressions?

Algebraic expressions are combinations of numbers, letters and operations. The letters represent unknown values, while the numbers are constants.

For example:
$3x + 5$
$2a − 7$
$4y + 3y$

In this lesson, we will learn how to simplify expressions by collecting like terms — one of the most important algebra skills at GCSE.

Example Question:

We will work through this step by step:

Simplify the expression:
$3x + 5 + 2x − 7$

Exam Tip

Always group the same types of terms together before combining them.

Look for:

Terms with the same letter
Terms with the same power
Numbers (constants)

Remember: You can only combine like terms.

Method — Simplifying Algebraic Expressions

We simplify expressions by collecting like terms. This means combining terms that are the same.

Follow these steps:

Identify like terms
Terms are alike if they have the same letters raised to the same powers.
Rearrange the expression
Put like terms next to each other.
Combine the coefficients
Add or subtract the numbers in front of the letters.
Combine constant terms
Add or subtract any standalone numbers.

Worked Example

Simplify:
$3x + 5 + 2x − 7$

Step 1: Identify like terms

Like terms are:

$3x$ and $2x$ (both contain $x$ )
$5$ and $-7$ (both are numbers)

Step 2: Rearrange the expression

$3x + 2x + 5 − 7$

Step 3: Combine $x$ terms

$3x + 2x = 5x$

Expression becomes:

$5x + 5 − 7$

Step 4: Combine constants

$5 − 7 = −2$

Final answer:

$5x − 2$

Always write your answer in its simplest form.

Check your solution (important habit)

Pick a value for $x$ to check both expressions give the same result.

Let $x = 1$

Original expression:

$3(1) + 5 + 2(1) − 7 = 3 + 5 + 2 − 7 = 3$

Simplified expression:

$5(1) − 2 = 5 − 2 = 3$

Both expressions give the same result for x = 1. Substitution is a useful check for mistakes, but matching at one value does not prove that two expressions are equal for every value of x. Here, collecting like terms using the rules of algebra establishes the simplification.

Think Like a Mathematician

Simplifying makes expressions easier to work with and helps reveal structure.

For example, the expression:

$4x + 3 − x$

can be simplified to:

$3x + 3$

This form is easier to evaluate, graph or substitute into equations.

Common mistakes to avoid

Combining unlike terms (for example, $x + x²$ cannot be simplified)
Forgetting negative signs
Mixing variables and constants incorrectly
Not rearranging first

Most errors occur when students rush and combine terms incorrectly.

Try one yourself

Simplify the following expression:

$4x + 9 − 2x + 3$

Hint: Rearrange first so like terms are together.

Collect like terms, keeping each term’s sign.

4x + 9 − 2x + 3 = 4x − 2x + 9 + 3

4x − 2x = 2x and 9 + 3 = 12.

Answer: 2x + 12

As a check, let x = 2: the original gives 8 + 9 − 4 + 3 = 16, and the simplified expression gives 4 + 12 = 16.

Frequently Asked Questions

What are like terms?

Like terms have exactly the same variables raised to the same powers.

For example:

$3x$ and $−5x$ are like terms

$2a²$ and $7a²$ are like terms

$x$ and $x²$ are NOT like terms

Why can we add $3x$ and $5x$ but not $3x$ and $5$ ?

Because $3x$ and $5x$ represent quantities of $x$ , while $5$ is just a number with no variable.

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