Year 9: Factorisation

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1. What Is factorisation?

Factorisation is the process of writing an expression as a product of its factors. It is the reverse of expanding brackets.

Example: 2x(x + 3) is the factorised form of 2x² + 6x.

2. Common factors

Look for the greatest common factor (GCF) of all terms and factor it out.

Example: 6x + 9 = 3(2x + 3)

Exercises

3. Factorising using the distributive law

Use the distributive law in reverse: ab + ac = a(b + c)

Example: x² + 5x = x(x + 5)

Exercises

4. Factorising trinomials (quadratics)

Trinomials are expressions with three terms, usually in the form ax² + bx + c.

To factorise, find two numbers that multiply to give ac and add to give b.

Example: x² + 7x + 10 = (x + 2)(x + 5)

Exercises

5. Difference of two squares

This special pattern is written as: a² − b² = (a − b)(a + b)

Example: x² − 9 = (x − 3)(x + 3)

6. Factorising by grouping

Group terms to find common factors within each group.

Example: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

7. Practice questions

1. Factorise: 12x + 8
2. Factorise: x² + 10x + 21
3. Factorise: x² − 16
4. Factorise: 3a + 6b − 2a − 4b

8. Solutions

1. 4(3x + 2)
2. (x + 3)(x + 7)
3. (x − 4)(x + 4)
4. Group: (3a − 2a) + (6b − 4b) = a + 2b

Practice!

Here are some exercise quizzes to further sharpen your skills in factorisation:

• Factorise difference of squares
• Factorisation