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Factorising Algebraic Expressions

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Factorising Algebraic Expressions

📚 Part 1: Factorising Single Bracket Expressions

Success Criteria: I can identify the greatest common factor and correctly factorise expressions with positive and negative terms.

1. Factorise: 6x + 9
2. Factorise: 4x² - 8x
3. Factorise: 3x² + 6x
4. Factorise: -5x³ + 10x²
5. Factorise: 2x⁴ - 8x²
6. Factorise: 12y² - 18y + 6

🔗 Part 2: Matching Expanded and Factorised Forms

Success Criteria: I can match expanded expressions with their factorised forms and explain my reasoning.

7. Match each expanded expression with its correct factorised form. Draw lines to connect them.
a) 15x² + 10x
b) 6x³ - 9x²
c) 8x² + 12x - 4
d) -4x² + 8x
i) 3x²(2x - 3)
ii) 5x(3x + 2)
iii) 4(2x² + 3x - 1)
iv) -4x(x - 2)
8. Choose the correct factorised form of 9x² - 12x:

3x(3x - 4)

9x(x - 12)

3(3x² - 4x)

x(9x - 12)

✏️ Part 3: Problem Solving and Reasoning

Success Criteria: I can explain the factorisation process and check my work by expanding.

9. Factorise: 7x³ - 14x² + 21x

Check your answer by expanding it back: _______________

10. A student factorised 6x² + 9x as 3(2x² + 3x). Explain what is wrong with this answer and write the correct factorisation.
11. Fill in the missing term: 4x² + _____ = 2x(2x + 5)
12. Explain in your own words: What is the relationship between factorisation and expansion?

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