A1AlgebraFoundation

Algebraic Notation

Algebra uses letters to stand for numbers we do not know yet. Learning the shorthand rules — and how to collect like terms — is the gateway to everything else in algebra.

25 min Video by Maths Genie AQA GCSE Maths

Simplifying AlgebraWatch the walkthrough, then read the notes below.

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What you'll learn

Use algebraic shorthand correctly
Collect like terms
Multiply terms together
Understand the difference between terms, expressions and equations

The shorthand rules

We write $3 \times n$ as $3 n$ , $n \times n$ as $n^{2}$ , and $n \div 4$ as $\frac{n}{4}$ . A number in front of a letter is the $coefficient$ .

Tip — Always write the number before the letter: $3 n$ , not $n 3$ .

Collecting like terms

$Like terms$ have exactly the same letters and powers. You can add or subtract them; unlike terms must stay separate.

1Group the a-terms:

4 a + 2 a = 6 a

2Group the b-terms:

3 b - b = 2 b

Answer

6 a + 2 b

Remember these

3 \times n = 3 n

Drop the times sign.

n \times n = n^{2}

A letter times itself.

Watch out for these

Adding unlike terms:

4 a + 3 b = 7 ab

Only collect like terms —

4 a + 3 b

cannot be simplified.

Writing

a + a = a^{2}

Adding gives

2 a

; multiplying gives

a^{2}

Key takeaways

Drop the × sign: 3 × n = 3n.
Collect only like terms (same letters and powers).
a + a = 2a, but a × a = a².

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