Simplifying expressions Revision Notes for AQA GCSE Maths

Simplifying expressions

What is simplifying expressions?

Simplifying expressions means rewriting algebraic expressions in their shortest possible form. You'll need to master this skill for your GCSE exam, as questions involving multiplication (×) and addition (+) symbols frequently appear.

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The key is to follow systematic rules that help you combine like terms and reduce expressions to their simplest form. Mastering these rules will make complex algebraic problems much more manageable.

Multiplying expressions

Multiplying expressions involves combining terms that are multiplied together. When you multiply algebraic terms, you need to handle numbers and letters separately.

Rules for multiplication

Follow these steps when multiplying expressions:

Step 1: Multiply the numbers first
Step 2: Then multiply the letters together
Step 3: Use indices for letters that appear multiple times

Examples of multiplication

When you see $10a × 3a$ , start with the numbers: $10 × 3 = 30$ . Then multiply the letters: $a × a = a²$ . So $10a × 3a = 30a²$ .

For $3x × 6t$ , multiply numbers first: $3 × 6 = 18$ . Then the letters: $x × t = xt$ . So $3x × 6t = 18xt$ .

Multiplying with algebra

Multiplying with algebra means writing letters next to each other to show multiplication, rather than using the × symbol.

Key rules

$ab = a × b$ - Letters written together mean multiplication
$y² = y × y$ - This reads as "y squared"
$n³ = n × n × n$ - This reads as "n cubed"

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Indices (also called powers) show how many times a letter is multiplied by itself. Instead of writing $n × n × n$ , you write $n³$ . This makes expressions much neater and easier to work with.

Dividing expressions

Dividing expressions involves splitting one algebraic term by another. The most effective method is to write the division as a fraction.

Rules for division

Follow these steps when dividing expressions:

Step 1: Write the division as a fraction
Step 2: Cancel any common number parts
Step 3: Cancel letters that appear on both top and bottom

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Examples of Division:

Example 1: For $8y ÷ 4$ , write as $\frac{8y}{4}$ . Cancel the numbers: $8 ÷ 4 = 2$ . You're left with $2y$ .

Example 2: For $36ab ÷ 9b$ , write as $\frac{36ab}{9b}$ . First cancel numbers: $36 ÷ 9 = 4$ . Then cancel the letter $b$ which appears on top and bottom. You're left with $4a$ .

Worked examples walkthrough

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Worked Examples: Simplifying Expressions

Example 1: Simplify $a × a × a$

Since we're multiplying the same letter three times, we use indices
$a × a × a = a³$

Example 2: Simplify $7x × 2y$

Multiply numbers: $7 × 2 = 14$
Multiply letters: $x × y = xy$
Answer: $14xy$

Example 3: Simplify $\frac{10pq}{2p}$ (or $10pq ÷ 2p$ )

Write as fraction: $\frac{10pq}{2p}$
Cancel numbers: $10 ÷ 2 = 5$
Cancel the letter $p$ from top and bottom
Answer: $5q$

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Key Points to Remember:

Always multiply numbers first, then deal with the letters
Letters written together mean multiplication - no × symbol needed
Use indices (powers) when the same letter appears multiple times
For division, write as a fraction and cancel common factors
Cancel letters that appear on both the top and bottom of fractions

Simplifying expressions (AQA GCSE Maths): Revision Notes