Expanding and Factorising - Worksheets, Questions and Revision

19 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 7)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Algebra

4.8 Expanding and Factorising

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Expand each bracket.

(a)4(x + 3)(1)

(b)5(2x - 1)(1)

(c)-3(x + 4)(1)

(Total for Question 1 is 3 marks)

Expand and simplify each expression.

(a)3(x + 2) + 2(x + 5)(2)

(b)6(x + 1) + 3(x - 2)(2)

(Total for Question 2 is 4 marks)

Factorise each expression fully.

(a)6x + 9(1)

(b)10x - 15(1)

(Total for Question 3 is 2 marks)

Factorise each expression fully.

(a)8x² - 12x(2)

(b)10x² + 15x(2)

(Total for Question 4 is 4 marks)

Expand and simplify each expression.

(a)(x + 3)(x + 5)(2)

(b)(x - 2)(x + 7)(2)

(c)(2x + 1)(3x - 4)(3)

(Total for Question 5 is 7 marks)

Expand and simplify (x + 4)²

(Total for Question 6 is 2 marks)

Which of these is the correct expansion of (x - 3)(x + 3) ?

A) x² - 9
B) x² + 9
C) x² - 6x - 9
D) x² - 6x + 9

(Total for Question 7 is 1 mark)

Factorise each expression.

(a)x² + 7x + 10(2)

(b)x² - 3x - 18(2)

(Total for Question 8 is 4 marks)

Factorise x² - 25

(Total for Question 9 is 1 mark)

Show that (x + 2)(x - 2) + 4 = x²

(Total for Question 10 is 2 marks)

A rectangle has length (x + 6) cm and width (x + 2) cm. The Find an expression, in its simplest form, for the area of the rectangle.

Diagram NOT accurately drawn

(Total for Question 11 is 3 marks)

Solve 3(x + 2) = 5(x - 4)

(Total for Question 12 is 3 marks)

Factorise each expression.

(a)2x² + 7x + 3(3)

(b)3x² - 5x - 2(3)

(Total for Question 13 is 6 marks)

Factorise 4x² - 9

(Total for Question 14 is 2 marks)

Factorise fully 4x² - 16

(Total for Question 15 is 2 marks)

Simplify fully (x² - 9)/(x + 3)

(Total for Question 16 is 2 marks)

Solve x² - 5x - 14 = 0 by factorising. Show your working.

(Total for Question 17 is 3 marks)

Show that (x + 1)(x + 2)(x + 3) = x³ + 6x² + 11x + 6

(Total for Question 18 is 4 marks)

A rectangular garden has length (x + 3) metres and width (x - 1) metres. The The area of the garden is 45 m².

Diagram NOT accurately drawn

(a)Show that x² + 2x - 48 = 0(2)

(b)By factorising, solve the equation to find the width of the garden.(3)

(Total for Question 19 is 5 marks)

Mark scheme · 4.8 Expanding and Factorising

Question 1

(a) B1 4x + 12 oe
(a) Answer: 4x + 12
(b) B1 10x - 5 oe
(b) Answer: 10x - 5
(c) B1 -3x - 12 oe
(c) Answer: -3x - 12

Question 2

(a) M1 expands both brackets, 3x + 6 and 2x + 10 oe
(a) A1 5x + 16 oe cao
(a) Answer: 5x + 16
(b) M1 expands both brackets, 6x + 6 and 3x - 6 oe
(b) A1 9x oe cao
(b) Answer: 9x

Question 3

(a) B1 3(2x + 3) cao
(a) Answer: 3(2x + 3)
(b) B1 5(2x - 3) cao
(b) Answer: 5(2x - 3)

Question 4

(a) M1 identifies common factor 4x
(a) A1 4x(2x - 3) cao, fully factorised
(a) Answer: 4x(2x - 3)
(b) M1 identifies common factor 5x
(b) A1 5x(2x + 3) cao, fully factorised
(b) Answer: 5x(2x + 3)

Question 5

(a) M1 at least 3 of the 4 terms correct, x², 5x, 3x, 15
(a) A1 x² + 8x + 15 oe cao
(a) Answer: x² + 8x + 15
(b) M1 at least 3 of the 4 terms correct, x², 7x, -2x, -14
(b) A1 x² + 5x - 14 oe cao
(b) Answer: x² + 5x - 14
(c) M1 at least 3 of the 4 terms correct, 6x², -8x, 3x, -4
(c) M1 correctly collects the x terms, -8x + 3x
(c) A1 6x² - 5x - 4 oe cao
(c) Answer: 6x² - 5x - 4

Question 6

M1 writes as (x+4)(x+4) and attempts to expand, at least 3 of 4 terms correct
A1 x² + 8x + 16 oe cao
Answer: x² + 8x + 16

Question 7

B1 A, x² - 9
Answer: A) x² - 9

Question 8

(a) M1 finds two numbers with sum 7 and product 10, namely 2 and 5
(a) A1 (x + 2)(x + 5) cao
(a) Answer: (x + 2)(x + 5)
(b) M1 finds two numbers with sum -3 and product -18, namely -6 and 3
(b) A1 (x - 6)(x + 3) cao
(b) Answer: (x - 6)(x + 3)

Question 9

B1 (x - 5)(x + 5) cao
Answer: (x - 5)(x + 5)

Question 10

M1 expands (x+2)(x-2) correctly to x² - 4
A1 cso, x² - 4 + 4 = x² shown with no errors
Answer: x² (shown)

Question 11

M1 sets up area = length x width, (x+6)(x+2)
M1 at least 3 of the 4 terms correct, x², 2x, 6x, 12
A1 x² + 8x + 12 cm² oe cao, with units
Answer: x² + 8x + 12 cm²

Question 12

M1 expands both sides correctly, 3x + 6 = 5x - 20 oe
M1 correct method to collect terms, 26 = 2x oe
A1 x = 13 cao
Answer: x = 13

Question 13

(a) M1 correct method, splits 7x using factors of 2x3=6 that sum to 7, namely 6x and x
(a) M1 correct partial factorisation seen, e.g. 2x(x+3) + 1(x+3)
(a) A1 (2x + 1)(x + 3) cao
(a) Answer: (2x + 1)(x + 3)
(b) M1 correct method, splits -5x using factors of 3x(-2)=-6 that sum to -5, namely -6x and x
(b) M1 correct partial factorisation seen, e.g. 3x(x-2) + 1(x-2)
(b) A1 (3x + 1)(x - 2) cao
(b) Answer: (3x + 1)(x - 2)

Question 14

M1 recognises difference of two squares, (2x)² - 3²
A1 (2x - 3)(2x + 3) cao
Answer: (2x - 3)(2x + 3)

Question 15

M1 takes out common factor 4, 4(x² - 4)
A1 4(x - 2)(x + 2) cao, fully factorised
Answer: 4(x - 2)(x + 2)

Question 16

M1 factorises the numerator, (x - 3)(x + 3)
A1 x - 3 oe cao, (x + 3) cancelled correctly
Answer: x - 3

Question 17

M1 finds two numbers with sum -5 and product -14, namely -7 and 2
A1 (x - 7)(x + 2) [= 0] cao
A1 x = 7 and x = -2 both cao
Answer: x = 7 or x = -2

Question 18

M1 expands (x+1)(x+2) correctly, x² + 3x + 2
M1 multiplies their quadratic by (x+3), at least 4 of the 6 terms correct
M1 collects like terms correctly, 3x² + 9x² combined and 2x + 9x combined
A1 cso, x³ + 6x² + 11x + 6 shown with no errors
Answer: x³ + 6x² + 11x + 6 (shown)

Question 19

(a) M1 correct area expression, (x+3)(x-1) = 45 oe, expanded to x² + 2x - 3 = 45
(a) A1 cso, correctly rearranged to x² + 2x - 48 = 0 with all steps shown
(a) Answer: x² + 2x - 48 = 0 (shown)
(b) M1 correct factorisation, (x+8)(x-6) = 0 oe, or valid alternative method
(b) A1 x = -8 or x = 6 both found
(b) A1 width = 5 m selected (dep), with reason that x = -8 is rejected as a length cannot be negative
(b) Answer: width = 5 m

Question 19

5 marks

Did your answer earn the marks?

Mark my answers

Expanding and Factorising - Worksheets, Questions and Revision

More on this topic

Next in this strand

4.8 Expanding and Factorising

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19