Question 1: Simplify the expression by factorising out the greatest common factor: 18x + 24.

Answer: 6(3x + 4)

Question 2: Factorise fully: 45y - 60.

Answer: 15(3y - 4)

Question 3: Find the common factor and factorise: 56a + 14b.

Answer: 14(4a + b)

Question 4: Simplify: 36m + 48n - 60p by factorising out the greatest common factor.

Answer: 6(6m + 8n - 10p)

Question 5: Factorise the expression: 81x^2 - 16.

Answer: (9x + 4)(9x - 4)

Question 6: Identify the common factor and factorise: 100p - 25q + 75r.

Answer: 25(4p - q + 3r)

Question 7: Explain why 12x + 18 is not fully factorised unless the common factor is extracted. Provide the fully factorised form.

Answer: Because the highest common factor of 12 and 18 is 6, the fully factorised form is 6(2x + 3).

Question 8: A bag contains 48 red apples and 60 green apples. If they are to be packed into boxes with the same number of apples, what is the greatest number of apples per box? Show your reasoning.

Answer: The greatest number of apples per box is the GCF of 48 and 60, which is 12.

Question 9: Construct the algebraic expression representing: 7 times a number plus 14, then factor out the common factor.

Answer: 7(x + 2)

Question 10: Identify and correct the mistake: Factoring 20x + 25y as 5(4x + 5y).

Answer: The mistake is that 5 is the greatest common factor of 20 and 25. The correct factorisation is 5(4x + 5y), which is correct. (Note: this is a trick question; the original is correct, but students should check GCF.)

Question 11: Extend the expression: Factorise 48x^2 + 72x + 24 and factor out the common factor completely.

Answer: 24(2x^2 + 3x + 1)