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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 .

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?

2 .

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

3 .

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

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 .

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

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 .

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

3 is a part of both 3x and 9

9 .

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?

10 .

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

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

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