Question 1: Factorise the expression 6x + 9.

Answer: 3(2x + 3)

Question 2: Factorise the expression 4a - 8b.

Answer: 4(a - 2b)

Question 3: Factorise 10m + 15n.

Answer: 5(2m + 3n)

Question 4: Simplify and factorise 8x + 12.

Answer: 4(2x + 3)

Question 1: Factorise 14y + 21z and explain why you can factor out 7.

Answer: 7(2y + 3z)

Question 2: Identify the mistake in the factorisation of 18a + 24b as 6(a + 4b).

Answer: Incorrect because 6 is not a common factor of 24b, only of 18a and 24b if 24b were 6 times 4b, but 6 times 4b is 24b, so this is correct. But if the mistake is in the process, the student might have incorrectly identified the common factor; the correct factor is 6, so the mistake might be in the interpretation.

Question 1: A rectangle has length 12x + 18 and width 6x. Find an expression for its area after factorising common factors.

Answer: Area = (12x + 18) * 6x = 6(2x + 3) * 6x

Question 1: Factorise the expression 15x^2 + 20x - 5.

Answer: 5(3x^2 + 4x - 1)

Question 2: Given the expression 9a^2b + 12ab^2, factorise completely and explain each step.

Answer: 3ab(3a + 4b)

Question 1: Factorise 20x + 25.

Answer: 5(4x + 5)

Question 2: Construct a factorised form of 8a + 16.

Answer: 8(a + 2)

Question 3: Explain why 12x + 18 cannot be fully simplified unless you factor out the GCD.

Answer: Because the GCD of 12x and 18 is 6, factoring out 6 simplifies the expression to 6(2x + 3).

Question 1: A student factors 20x + 25 as 5(4x + 5), claiming they have fully simplified. Is this correct? If not, explain and correct.

Answer: Yes, the factorisation is correct because 5 is the GCD of 20 and 25, and both terms are divisible by 5.

Question 2: A student attempts to factorise 18a + 24b as 6(a + 4b). Is this correct? If not, what is the mistake?

Answer: Incorrect because the common factor of 18a and 24b is 6, but the second term should be 6a + 8b, not 6(a + 4b). The correct factorisation is 6(3a + 4b).