What is 5x − 2x + 4 simplified?

3x + 4. Only the x terms combine.

What is 3(x + 4) expanded?

3x + 12. Multiply both terms by 3.

What is (x + 1)(x + 5) expanded?

x² + 6x + 5. x² + 5x + x + 5.

What is x² + 7x + 10 factorised?

(x + 2)(x + 5). 2 × 5 = 10 and 2 + 5 = 7.

What is x² − 16 factorised?

(x + 4)(x − 4). It is the difference of two squares.

Expanding and factorising · Cambridge IGCSE Mathematics

In plain words

Algebra is arithmetic with a letter standing in for a number you don't know yet. Expanding means multiplying brackets out. Factorising is the reverse: putting brackets back in. Being quick at both makes almost everything else in algebra easier.

Three things to know

Collect like terms: 3x + 2y − x + 5y = 2x + 7y. To expand a bracket, multiply everything inside by what is outside: 4(2x − 3) = 8x − 12.
Two brackets: multiply each term in the first by each term in the second. (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
Factorise by taking out what is common: 6x + 9 = 3(2x + 3). A quadratic goes into two brackets: x² + 5x + 6 = (x + 2)(x + 3). The difference of two squares: x² − 9 = (x + 3)(x − 3).

Worked example

Factorise x² − x − 12.

Look for two numbers that multiply to give −12 and add to give −1.
−4 and 3 work: −4 × 3 = −12 and −4 + 3 = −1.
(x − 4)(x + 3).

Tips and tricks

Check factorising by expanding your answer: you should get back to where you started.
A minus outside a bracket changes every sign inside: −(x − 3) = −x + 3.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Expanding and factorising: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is 5x − 2x + 4 simplified?
- 7x
- 3x + 4 (the answer)
- 7x + 4
- 3x − 4
Only the x terms combine.
What is 3(x + 4) expanded?
- 3x + 4
- x + 12
- 3x + 12 (the answer)
- 3x + 7
Multiply both terms by 3.
What is (x + 1)(x + 5) expanded?
- x² + 5
- x² + 5x + 6
- x² + 6x + 5 (the answer)
- 2x + 6
x² + 5x + x + 5.
What is x² + 7x + 10 factorised?
- (x + 1)(x + 10)
- (x + 2)(x + 5) (the answer)
- (x + 3)(x + 4)
- x(x + 17)
2 × 5 = 10 and 2 + 5 = 7.
What is x² − 16 factorised?
- (x − 4)²
- (x − 8)(x + 2)
- (x + 4)(x − 4) (the answer)
- (x − 16)(x + 1)
It is the difference of two squares.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 8 marks. Write your answers on paper, then check them.

Expanding and factorising

Cambridge IGCSE Mathematics 0580 · 8 marks · papermunch.org

Name ______________________________ Date ______________

Expand and simplify (x + 4)(x − 2).[2]
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x² + 2x − 8.
I got this one
Factorise 10x² − 15x.[2]
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5x(2x − 3).
I got this one
Factorise x² − 25.[2]
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(x + 5)(x − 5).
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Find the value of 3a² − b when a = 2 and b = 5.[2]
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7. 3 × 4 − 5.
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Answers: Expanding and factorising

1. x² + 2x − 8.
2. 5x(2x − 3).
3. (x + 5)(x − 5).
4. 7. 3 × 4 − 5.