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Level 7-8 Algebra - Factorisation

Factorising expressions makes algebra simpler. Spot common factors, take out brackets, and rewrite terms to solve KS3 problems faster and with fewer mistakes.

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Fascinating Fact:

Factorisation is also used in physics for simplifying formulas such as force = mass × acceleration, where common terms can cancel.

In KS3 Maths, factorisation helps you rewrite algebraic expressions efficiently. You’ll extract common factors, factorise single brackets (like ax + ay = a(x + y)), and simplify expressions to make equations easier to solve.

Key Terms

Factor: A quantity multiplied by another to make a product (e.g., 3 and 4 are factors of 12).
Common factor: A number or term that divides every term in an expression.
Factorisation: Rewriting an expression as a product, often by taking out the highest common factor.

Frequently Asked Questions (Click to see answers)

What does factorising mean in KS3 algebra?

Factorising means writing an expression as a product. For example, 8x + 12 becomes 4(2x + 3) after taking out the highest common factor 4.

How do I factorise a simple expression like 6x + 9?

Find the highest common factor of 6x and 9, which is 3. Divide each term by 3 to get 3(2x + 3).

What is the difference between expanding and factorising?

Expanding removes brackets (e.g., 3(x + 2) → 3x + 6). Factorising adds brackets by reversing that process (e.g., 3x + 6 → 3(x + 2)).

Try These Related Quizzes

1 .

What is the correct answer when you factorise 4x²y³ + 8xy²?

4xy²(x + 2)

4xy²(xy + 2)

4xy²(xy + 4)

4xy²(y + 2)

Can you see why?

2 .

What are the highest common factors in 4x²y³ + 8xy²?

2 and x and y²

4 and x

4 and x and y²

4 and y

4 is the highest common factor of 4 and 8, x is the highest common factor of x and x² and y² is the highest common factor of y² and y³

3 .

Factorise the following expression into a pair of linear brackets x² + 8x + 12

(x - 2)(x - 6)

(x - 2)(x + 6)

(x + 2)(x - 6)

(x + 2)(x + 6)

Can you see the pattern?

4 .

What is the correct answer when you factorise x² -5x?

x(x - 5)

x(x + 5)

x(x² - 5)

x(x² + 5)

The common factor is placed outside the brackets

5 .

Factorise the following expression into a pair of linear brackets x² - 9x + 8

(x + 1)(x + 8)

(x +1)(x - 8)

(x -1)(x - 8)

(x -1)(x + 8)

After you have factorised several expressions you will begin to see patterns emerging that enable you to quickly arrive at the correct answer

6 .

What is the correct answer when you factorise 3x - 9?

3(x - 3)

3(x + 3)

x(3 - 3)

x(3 + 3)

The common factor is placed outside the brackets

7 .

What is the common factor in the terms x² -5x?

-5

x is a part of both x² and 5x

8 .

Factorise the following expression into a pair of linear brackets x² + 7x + 6

(x + 1)(x + 6)

(x - 1)(x + 6)

(x + 1)(x - 6)

(x - 1)(x - 6)

To check each of the answers it is necessary to multiply out the brackets. Remember that each term in each bracket is multiplied by each term in the other bracket

9 .

What is the common factor in the terms 3x - 9?

3 is a part of both 3x and 9

10 .

Factorise the following expression into a pair of linear brackets x² - 5x - 6

(x - 1)(x - 6)

(x - 1)(x + 6)

(x + 1)(x - 6)

(x + 1)(x + 6)

The more often you factorise, the easier it will get

You can find more about this topic by visiting BBC Bitesize - Factorising

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)