Factorising Algebraic Expressions

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📚 Understanding Factorising

What is factorising? Factorising means writing an algebraic expression as a product of its factors. We look for the greatest common factor (GCF) and "take it out" using brackets.

Example: 5x - 35 = 5(x - 7)

Step 1: Find the GCF of 5x and 35 → GCF = 5
Step 2: Divide each term by the GCF → 5x ÷ 5 = x, 35 ÷ 5 = 7
Step 3: Write as GCF × (remaining terms) → 5(x - 7)

1. What is the greatest common factor (GCF) of 12x and 18?

2. Which expression is correctly factorised?

8y + 16 = 8(y + 2)

6a - 12 = 2(3a - 6)

10m + 5 = 5(2m)

9x - 27 = 3(3x - 24)

✏️ Factorising Practice

3. Factorise: 6x + 12

4. Factorise: 10y - 25

5. Factorise: 8a + 32

6. Factorise: 15m - 45

7. Factorise: 4p + 28

8. Check your answer to Question 7 by expanding 4(p + 7). Show your working:

🌟 Real-World Applications

9. A school is organising sports equipment. They have 18 basketballs and 12 soccer balls to distribute equally among classes. If each class gets the same number of each type of ball, what is the maximum number of classes that can receive equipment? Write this as a factorising problem.

10. The cost of hiring a venue is $7x + $21, where x is the number of hours. Factorise this expression and explain what the factorised form tells us about the cost structure.

11. A rectangular garden has an area of 9w + 36 square metres. If the width is 9 metres, what is the length? Use factorising to solve this problem.