plumiSimplifying, expanding and factorising: Edexcel GCSE Maths questions
Every Edexcel GCSE Maths exam question on A4 Simplifying, expanding and factorising, 2017–2025, with its mark scheme and examiner’s report.
Find questions997
Exam
All years
Calculator
All 52 questions on Simplifying, expanding and factorising, as a list
- June 2025, Paper 1H, Q7 (6 marks): (a) Simplify 3 2 m 2 m x – 8 (b) Solve 7 + x 5 2 (c) Solve 9 < 2y + 4 < 12
- June 2025, Paper 2H, Q9 (2 marks): 3x n for all the values of x that are not zero. Find the value of a, the value of b and the value of n. a = b = n =
- June 2025, Paper 2H, Q13 (3 marks): Show that (2x + 3)(x – 1)(x + 2) can be written in the form ax 3 + bx 2 + cx + d where a, b, c and d are integers.
- June 2025, Paper 3H, Q2 (3 marks): Ben is trying to make m the subject of p = m 3 + 5 Here is his working. p – 5 = m 3 3 × p – 5 = m m = 3 p – 5 Ben’s answer is wrong. (a) What mistake has Ben ma
- June 2025, Paper 3H, Q17 (3 marks): Solve 1 x x 3 1 3 1 x =
- November 2024, Paper 1H, Q11 (5 marks): Kate was asked to factorise x 2 + 5x + 6 in the form (x + a)(x + b) Kate says, “The sum of a and b must be 6 and the product of a and b must be 5” (a) Explain w
- November 2024, Paper 2H, Q17 (3 marks): Show that 6 x y 1 2 y 7 x simplifies to k y where k is an integer. xy x xy 10 2 5
- November 2024, Paper 3H, Q9 (3 marks): (a) Simplify fully 2x 3y 5 × 7x 2y (b) Simplify (m2)–3
- June 2024, Paper 1H, Q14 (3 marks): Expand and simplify (3x – 1)(2x + 3)(x – 5)
- June 2024, Paper 3H, Q15 (6 marks): (a) Simplify fully ( a − 3 ) a 5 ( − 3 ) 2 + 11k – 4 (b) Factorise 3k 2 x x (c) Simplify fully 4 2 2 x x 3 x 3
- November 2023, Paper 1H, Q17 (4 marks): (a) Factorise 6x2 – 5x – 4 (b) Hence, or otherwise, solve 6x2 – 5x – 4 < 0
- November 2023, Paper 2H, Q1 (6 marks): (a) Expand and simplify 3(2y − 5) + 7 (y + 2) (b) Factorise fully 6x2 + 15x (c) Make g the subject of the formula f = 3g + 11
- November 2023, Paper 2H, Q9 (3 marks): Expand and simplify (x + 7)(x – 2)(x + 3)
- November 2023, Paper 2H, Q20 (4 marks): Write x x 14 2 6 56 in the form ax + b 2 x 4 where a, b, c and d are integers. x x 3 21 2 3 cx + d
- November 2023, Paper 3H, Q23 (4 marks): Given that 2 43 = where x > 0 and y > 0 2 2 4 x - y 11 find, in its simplest form, the ratio x : y
- June 2023, Paper 2H, Q14 (3 marks): Show that x − x − 6 2 can be written in the form ax + b where a, b, c and d x x 2 − 5 − 3 cx d 2 + are integers.
- June 2023, Paper 3H, Q1 (4 marks): (a) Simplify (m 2 ) 3 5×x 8 (b) Simplify x (c) Expand 4p ( p 2 + 3p)
- June 2023, Paper 3H, Q12 (3 marks): Show that (x – 1)(x + 3)(x – 5) can be written in the form ax 3 + bx 2 + cx + d where a, b, c and d are integers.
- June 2023, Paper 3H, Q15 (3 marks): (a) Factorise a 2 – b 2 40 – 1 is the product of two consecutive odd numbers. (b) Show that 2
- June 2023, Paper 3H, Q21 (4 marks): Solve 1 x x 4 2 2
- June 2023, Paper 3H, Q24 (5 marks): There is a total of y counters in a box. There are x pink counters and 5 blue counters in the box. The rest of the counters are green. x : y = 1 : 3 Freda takes
- November 2022, Paper 3H, Q10 (1 mark): Peter has to subtract (x2 − 2x − 4) from (x2 + 3x + 5) Here is his working (x2 + 3x + 5) − (x2 − 2x − 4) = x2 + 3x + 5 − x2 − 2x − 4 = x + 1 Explain what is wro
- November 2022, Paper 3H, Q14 (5 marks): (a) Simplify fully (3x5y6)4 (b) Expand and simplify (x + 2)(x − 3)(x + 4)
- November 2022, Paper 3H, Q22 (3 marks): 2 3 4 + − 3 25 where a and b are integers. x − x + x − 5 5 2 Work out the value of a and the value of b. You must show all your working. a = b =
- June 2022, Paper 1H, Q19 (4 marks): Solve + = 1 x − x − 2 1 1 Give your answer in the form p ± q where p and q are integers. 2
- June 2022, Paper 2H, Q1 (5 marks): (a) Simplify (x3)5 (b) Expand and simplify 4(x + 3) + 7(4 − 2x) (c) Factorise fully 15x3 + 3x2y
- June 2022, Paper 3H, Q7 (3 marks): The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm. 2x Q U T 4x S R V 3x 5 The area of trapezium QUVR is A cm2 Show th
- June 2022, Paper 3H, Q14 (5 marks): (a) Factorise fully 4p2 − 36 (b) Show that (m + 4)(2m − 5)(3m + 1) can be written in the form am3 + bm2 + cm + d where a, b, c and d are integers.
- June 2022, Paper 3H, Q19 (4 marks): Show that − − 1 x + x − x − 2 2 4 2 where a and b are integers.
- November 2021, Paper 1H, Q14 (3 marks): Here is a shape with all its measurements in centimetres. x + 1 4 x + 11 2x + 6 The area of the shape is A cm2 Show that A = 2x2 + 24x + 46
- November 2021, Paper 1H, Q15 (3 marks): Show that 4 3 3 + where a, b and c are integers. x cx 2 5
- November 2021, Paper 2H, Q12 (3 marks): Expand and simplify (x – 2)(3x + 2)(2x + 3)
- November 2021, Paper 3H, Q22 (3 marks): Show that ÷ can be written in the form where r is x x r x − x − + 2 ( ) ( 9 144 ) 3 ( 4 ) an integer.
- November 2020, Paper 3H, Q12 (6 marks): (a) Express 4 as a single fraction in its simplest form. x x 2 (b) Expand and simplify (x − 3)(2x + 3)(4x + 5) .
- November 2019, Paper 1H, Q7 (3 marks): (a) Simplify (p2)5 (b) Simplify 12x7y3 ÷ 6x3y
- November 2019, Paper 1H, Q13 (3 marks): (a) Write x x as a single fraction in its simplest form. (b) Factorise (x + y)2 + 3(x + y)
- November 2019, Paper 2H, Q15 (3 marks): Expand and simplify (3x + 2)(2x + 1)(x
- November 2019, Paper 3H, Q1 (4 marks): (a) Expand and simplify (x + 5)(x – 9) (b) Factorise fully 9x2 + 6x
- November 2019, Paper 3H, Q22 (4 marks): Show that x simplifies to ax where a is an integer. x x x
- June 2019, Paper 2H, Q13 (4 marks): Show that 6 + ( x 5 ) ÷ where a, b, c and d are integers. + ⎣⎢ ⎦⎥ x 1 cx d − −
- June 2019, Paper 3H, Q18 (6 marks): (a) Show that (2x 1)(x 3)(3x 7) can be written in the form ax3 bx2 cx d where a, b, c and d are integers. 9 2 ( ) (b) Solve 1 x − 25
- November 2018, Paper 1H, Q10 (3 marks): (a) Simplify x − 5 ( 1 2 ) E )DFWRULVHIXOO\ í\࣠2
- November 2018, Paper 2H, Q12 (6 marks): (a) Write 4 − 9 2 + where a, b, c and d are integers. × cx d x x 2 x 6 + 9 − 3 + 3 1 4 (b) Express as a single fraction in its simplest form. + − x x x + 1 − 2
- November 2018, Paper 3H, Q9 (8 marks): (a) Expand and simplify (x – 2)(2x + 3)(x + 1) 4 n y × y − 3 = y 2 y (b) Find the value of n. (c) Solve 5x2 – 4x – 3 = 0 Give your solutions correct to 3 signif
- June 2018, Paper 1H, Q15 (4 marks): (a) Factorise a2íb2 (b) Hence, or otherwise, simplify fully (x2 + 4)2 – (x2 – 2)2
- June 2018, Paper 1H, Q17 (3 marks): Simplify fully 3 − 8 − 3 x 2 x 2 − 6
- June 2018, Paper 2H, Q1 (5 marks): (a) Simplify m3× m4 (b) Simplify (5np3)3 9 4 (c) Simplify 32 q r 3 4 q r
- June 2018, Paper 3H, Q2 (2 marks): Expand and simplify 5( p + 3) – 2(1 – 2p)
- June 2017, Paper 1H, Q4 (3 marks): 3 cm x cm A B 3 cm x cm D C The area of square ABCD is 10 cm2. Show that x2 + 6x = 1
- June 2017, Paper 1H, Q10 (3 marks): Show that (x + 1)(x + 2)(x + 3) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are positive integers.
- June 2017, Paper 2H, Q19 (4 marks): 2 − − 2 x 3 x 3 x 9 − + − where a and b are integers. Work out the value of a and the value of b. a = b =
- June 2017, Paper 3H, Q14 (6 marks): (a) Simplify 2 x x 2 − 5 − 12 15 ( t − 2 v ) (b) Make v the subject of the formula w = v
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel GCSE Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.