Simplifying expressions Revision Notes for Edexcel GCSE Maths

Simplifying expressions

When working with algebra, you'll often need to simplify expressions that contain both numbers and letters. This involves following specific rules to make expressions as simple as possible.

Multiplying expressions

Multiplying expressions means combining terms that are multiplied together. This is one of the fundamental skills in algebra that you'll use constantly.

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Steps for Multiplying Expressions:

Step 1: multiply the numbers first Always start by multiplying any numerical parts of the expression together.

Step 2: multiply the letters After dealing with numbers, multiply the letter parts. When the same letter appears multiple times, use indices (also called powers) to show this.

Key rules for indices:

$y \times y = y^2$ (say "y squared")
$n \times n \times n = n^3$ (say "n cubed")

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Worked Examples: Multiplying Expressions

Example 1: $10a \times 3a$

First multiply numbers: $10 \times 3 = 30$
Then multiply letters: $a \times a = a^2$
Answer: 30a²

Example 2: $3s \times 6t$

First multiply numbers: $3 \times 6 = 18$
Then multiply letters: $s \times t = st$
Answer: 18st

Dividing expressions

Dividing expressions involves splitting one expression by another. This process uses fractions and cancelling, which are essential techniques in algebra.

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Steps for Dividing Expressions:

Step 1: write the division as a fraction Transform the division into fraction form with the first expression on top and the second on the bottom.

Step 2: cancel number parts Divide the numbers on the top and bottom by their common factors.

Step 3: cancel matching letters If the same letter appears on both the top and bottom of the fraction, you can cancel them out.

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Worked Examples: Dividing Expressions

Example 1: $8y \div 4$

Write as fraction: $\frac{8y}{4}$
Cancel the numbers: $8 \div 4 = 2$
Answer: 2y

Example 2: $36ab \div 9b$

Write as fraction: $\frac{36ab}{9b}$
Cancel numbers: $36 \div 9 = 4$
Cancel the letter b from top and bottom
Answer: 4a

Multiplying with algebra

When working with algebraic terms, there are some important concepts that make calculations much easier once you understand them.

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Key Concepts for Algebraic Multiplication:

Multiplying letters together You can multiply letters in algebra by simply writing them next to each other. For example: $ab = a \times b$

Using indices for repeated letters When the same letter is multiplied by itself multiple times:

Two identical letters: $y \times y = y^2$ (y squared)
Three identical letters: $n \times n \times n = n^3$ (n cubed)

Practice examples

Here are some worked examples to help you understand the process and build your confidence with these techniques:

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Worked Example 1: Simplifying Repeated Letters Simplify $a \times a \times a$

This is the same letter three times
Answer: a³

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Worked Example 2: Multiplying Different Terms Simplify $7x \times 2y$

Multiply numbers first: $7 \times 2 = 14$
Then multiply letters: $x \times y = xy$
Answer: 14xy

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Worked Example 3: Division with Cancellation Simplify $10pq \div 2p$

Write as fraction: $\frac{10pq}{2p}$
Cancel numbers: $10 \div 2 = 5$
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
Use indices notation when the same letter is repeated ( $y^2$ for $y \times y$ , $n^3$ for $n \times n \times n$ )
For division, write as a fraction and cancel matching parts from top and bottom
Letters can be multiplied by simply writing them next to each other ( $ab = a \times b$ )
Practice cancelling - if the same letter appears on top and bottom of a fraction, it cancels out

Simplifying expressions (Edexcel GCSE Maths): Revision Notes