Simplifying, expanding and factorising: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on A4 Simplifying, expanding and factorising, 2017–2025, with its mark scheme and examiner’s report.

All 63 questions on Simplifying, expanding and factorising, as a list

June 2025, Paper 1H, Q24 (4 marks): Prove that x x x − − − 4 2 60 15 2 1 × 1 6 3 x − can never be positive.
June 2025, Paper 2H, Q6 (1 mark): Circle the expression which is a factor of 3x + 15 3x x + 12 x + 5 x + 15
June 2025, Paper 3H, Q20 (3 marks): (a) Factorise fully 3n2 + 5n + 2 Answer 20 (b) A sequence has nth term 3n2 + 5n + 2 Are any of the terms in the sequence a prime number? Tick a box. Yes No Give
November 2024, Paper 1H, Q19 (5 marks): (a) Expand and simplify fully (x + 2)(2x + 3)(3x + 4) Answer 19 (b) Use your answer from part (a) to work out 102 × 203 × 304 Answer
November 2024, Paper 2H, Q11 (3 marks): Here are three terms. xy x2 5y2 Alec multiplies two of these terms. Work out the three possible fully simplified answers. Answer Answer Answer
November 2024, Paper 3H, Q11 (2 marks): Factorise fully 12t + 4t3 Answer
November 2024, Paper 3H, Q20 (2 marks): Factorise fully 3x2 + 23x + 30 Answer
June 2024, Paper 2H, Q19 (5 marks): (a) Show that 4x(3x + 2) – 2x2 5 6 x   −     – 6x 7 3 x   +     simplifies to an integer. 19 (b) Factorise 8x2 – 18x – 35 Answer
November 2023, Paper 1H, Q4 (1 mark): Simplify a + 3a ÷ a Answer
November 2023, Paper 1H, Q11 (2 marks): Factorise x2 + 2x – 24 Answer
November 2023, Paper 2H, Q1 (1 mark): Expand 5x(x2 + 3) Answer
November 2023, Paper 2H, Q22 (1 mark): Factorise 25a2 – b2 Answer
November 2023, Paper 2H, Q24 (3 marks): Simplify fully 2 8 4 5 x x + × 2 3 14 7 x x + You must show your working. Answer
November 2023, Paper 3H, Q18 (3 marks): Simplify 3 5 4) ( 4) 2( + + x x Give your answer in the form ax2 + bx + c where a, b and c are integers. Answer
November 2023, Paper 3H, Q22 (2 marks): Write 2 2 7 a – a 3 5 as a single fraction in its simplest form. Answer
June 2023, Paper 1H, Q8 (2 marks): Expand and simplify fully 5(3x + 4) – 2(x – 1) Answer
June 2023, Paper 2H, Q15 (2 marks): Expand (x2 – 9xy)(2x + 5y) Answer
June 2023, Paper 2H, Q25 (3 marks): Show that 2 5 − − x x + 2 5 + + x x simplifies to ax b x − − 2 2 4 where a and b are integers.
November 2022, Paper 1H, Q15 (4 marks): Show that (3x + 4)(2x – 5) – 11x(x – 2) + 5(x2 – 3x – 1) simplifies to an integer.
November 2022, Paper 2H, Q22 (2 marks): Factorise fully x3 – 49x Answer
November 2022, Paper 3H, Q3 (1 mark): Expand 6x2(x3 + 2) Circle your answer. 6x5 + 2 6x6 + 2 6x5 + 12x2 6x6 + 12x2
November 2022, Paper 3H, Q22 (4 marks): Simplify fully 2 1 x + + 7 5 3 x − + 4x Give your answer as a single fraction. Answer
June 2022, Paper 1H, Q24 (6 marks): (a) Simplify fully a 6 – a 4 11 Answer 24 (b) Simplify fully (y2 – 3y) × y y y + + − 2 2 10 21 9 Answer
June 2022, Paper 2H, Q23 (2 marks): Factorise 3x2 – 16x – 12 Answer
June 2022, Paper 3H, Q13 (1 mark): Simplify 5 a + 5 a Circle your answer. 5a 5a2 2 5 a 10 a
June 2022, Paper 3H, Q27 (3 marks): Expand and simplify fully (x – 3)(x – 4)(x + 8) Answer
November 2021, Paper 1H, Q14 (1 mark): Simplify x 3 + x 4 Circle your answer. x 7 x 2 7 x 12 2 12 x
November 2021, Paper 1H, Q15 (3 marks): (x + a)(x + 3a) ≡ x2 + bx + 75 Work out the two possible values of b. Answer and
November 2021, Paper 2H, Q1 (1 mark): Circle the factor of x2 – 5x x – 1 –5x x – 5 5x
November 2021, Paper 3H, Q4 (1 mark): Factorise x2 – 64 Circle your answer. (x + 8)2 (x – 8)2 (x + 8)(x – 8) x(x – 64)
November 2021, Paper 3H, Q25 (3 marks): Expand and simplify fully (x – 3)(x + 2)(x + 5) Answer
November 2020, Paper 1H, Q13 (3 marks): (a) s and t are positive integers. (x + s)(x – t) is expanded and simplified. The answer is x2 + kx – 40 where k is a positive integer. Work out the smallest po
November 2020, Paper 1H, Q19 (1 mark): Circle the expression that is equivalent to 5 x + 10 x 10 3x 15 2x 25 x x2 50
November 2020, Paper 1H, Q28 (2 marks): Factorise fully 144 – 4x2 Answer
November 2020, Paper 2H, Q19 (3 marks): a and b are positive values. Show that 7 2 3 8 6 2 + − + + − a b a a b a b always simplifies to the same value.
November 2020, Paper 2H, Q25 (2 marks): Factorise 3x2 + 11x – 20 Answer
November 2020, Paper 2H, Q29 (5 marks): Solve 1 4 5 + x = 3 2 2 + x x Give your solutions to 3 significant figures. You must show your working. Answer
November 2020, Paper 3H, Q10 (2 marks): Expand and simplify fully 4(2c + 3) – (5c – 1) Answer
November 2020, Paper 3H, Q13 (3 marks): (a) Simplify 8 25a × 5 2a Give your answer as a single fraction in its simplest form. Answer 13 (b) Sofia is trying to simplify 6 10 2 + c Her method is divide
November 2019, Paper 1H, Q23 (5 marks): (a) Factorise 5x2 + 6x – 8 Answer 23 (b) Simplify fully 4 14 9 2 2 − + + x x x Answer
November 2019, Paper 2H, Q1 (1 mark): Expand 4x2(3x + 5) Circle your answer. 32x3 12x3 + 20x2 7x3 + 9x2 12x2 + 5
November 2019, Paper 3H, Q3 (1 mark): (2x – 4)(3x + 5) is expanded and simplified. Circle the term which is part of the answer. 2x –2x 22x –22x
June 2019, Paper 1H, Q16 (3 marks): Simplify fully 2 4 8 12 6 − − x x x Answer
June 2019, Paper 1H, Q18 (3 marks): Here is an identity. x2 – y2 ≡ (x + y)(x – y) 18 (a) Use the identity to work out the value of 1932 – 72 You must show your working. Answer 18 (b) Factorise 100
June 2019, Paper 2H, Q26 (3 marks): (x + 5)(x + 2)(x + a) ≡ x3 + bx2 + cx – 30 Work out the values of the integers a, b and c. a = b = c =
June 2019, Paper 3H, Q15 (3 marks): Simplify fully 3 2 5 × a b c cd ab Answer
November 2018, Paper 1H, Q3 (1 mark): Simplify 16a2 ÷ a + 3a × 2 Circle your answer. 22a 8a 38a 2a
November 2018, Paper 2H, Q22 (3 marks): Simplify fully 6 3 4 3 5 − − x x x Answer
November 2018, Paper 3H, Q17 (1 mark): w = x 5 3 Circle the expression for w2 2 10 6 x 2 25 9 x x 10 6 x 25 9
June 2018, Paper 1H, Q3 (1 mark): Circle the expression that is equivalent to 3a – a × 4a + 2a 8a2 + 2a 12a2 5a – 4a2 3a – 6a2
June 2018, Paper 1H, Q27 (4 marks): (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b
June 2018, Paper 2H, Q13 (3 marks): Show that, for x ≠ –1 4 4 8 8 2 + − x x simplifies to the form ax + b where a and b are integers.
June 2018, Paper 3H, Q18 (3 marks): Show that, for x ≠ 0 x x 3 4 + – x 2 5 can be written in the form cx b ax + where a, b and c are integers. Answer
November 2017, Paper 1H, Q5 (3 marks): (a) Factorise x2 – 100 Answer 5 (b) Solve 7x + 6 > 1 + 2x Answer
November 2017, Paper 2H, Q11 (1 mark): Circle the expression that is equivalent to 3 6 3 2 2 + x x 3 2 2 2 + x x 1 6 2 2 + x x 1 2 2 2 + x x 2 1 + x2
November 2017, Paper 2H, Q16 (4 marks): (a) Factorise fully 9y3 – 6y Answer 16 (b) Factorise 3x2 – 22x + 7 Answer
November 2017, Paper 2H, Q27 (6 marks): Solve 4 x – 2 2 + x x = 1 Give your solutions to 2 decimal places. You must show your working. Answer
November 2017, Paper 3H, Q5 (2 marks): Multiply out and simplify 2 ) 8 ( − x Answer
November 2017, Paper 3H, Q18 (4 marks): Expand and simplify (3x2 + 2)(2x + 5) – 6x(x2 – 3) Answer
June 2017, Paper 1H, Q26 (4 marks): Expand and simplify (x − 4)(2x + 3y)2 Answer
Specimen, Paper 1H, Q12 (4 marks): ABCH is a square. HCFG is a rectangle. CDEF is a square. They are joined to make an L-shape. Show that the total area of the L-shape, in cm2, is x 2 + 9x + 27 3
Specimen, Paper 2H, Q3 (1 mark): Circle the expression that is equivalent to 2a + 5a  4a – a a + 20a2 21a2 28a2 – a 2a + 15a2
Specimen, Paper 3H, Q17 (2 marks): Factorise 3x2 + 14x + 8 Answer

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