Expanding Double Brackets - Worksheets, Questions and Revision

18 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Algebra

KS3.M-A13 Expanding Double Brackets

AQA KS3.M-A13 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Expand each pair of brackets. Write your answer in fully simplified form.
(a)Expand (x + 3)(x + 5).(1)
(b)Expand (2x - 1)(x + 4).(1)
(c)Expand (x - 2)(x - 6).(1)
(d)Expand (3x + 2)(x - 5).(1)
2
Expand and simplify: (x + 7)(x - 2).
(single)(x + 7)(x - 2)(3)
3
Expand and simplify: (2x + 3)(2x - 1).
(single)(2x + 3)(2x - 1)(3)
4
Square the binomial and simplify: (x + 6)2.
(single)(x + 6)2(4)
5
Expand and simplify: (3x - 2)2.
(single)(3x - 2)2(3)
6
Expand and simplify: (x + 4)(2x + 5).
(single)(x + 4)(2x + 5)(4)
7
Expand and simplify: (x - 3)(3x + 2).
(single)(x - 3)(3x + 2)(3)
8
Expand and simplify: (4x + 1)(x - 2).
(single)(4x + 1)(x - 2)(3)
9
Expand and simplify: (x + 2)(x2 + x + 3). Note: multiply a binomial by a trinomial.
(single)(x + 2)(x2 + x + 3)(4)
10
Expand and simplify: (2x - 3)(x2 + 2x - 1).
(single)(2x - 3)(x2 + 2x - 1)(3)
11
Expand and simplify then collect like terms: (x + 1)(x - 2) + (x - 3)(x + 4).
(single)(x + 1)(x - 2) + (x - 3)(x + 4)(3)
12
Expand and simplify: (x + 5)(x - 5).
(single)(x + 5)(x - 5)(2)
13
Without expanding fully, state the coefficient of x2 in the expansion of (3x + 2)(5x - 1).
(single)Find the coefficient of x2 in (3x + 2)(5x - 1).(2)
14
Expand and simplify fully: (x + 2)(x - 3) - (x - 1)(x + 5).
(single)(x + 2)(x - 3) - (x - 1)(x + 5)(3)
15
A rectangle has length (x + 3) metres and width (2x - 1) metres. Expand and simplify an expression for its area.
(single)Area = (x + 3)(2x - 1). Expand and simplify.(4)
16
Find the expanded form of (ax + 2)(2x - b) and give the coefficient of x in terms of a and b.
(single)(ax + 2)(2x - b)(4)
17
A student expands (x + 4)(x + k) and obtains x2 + (k + 4)x + 4k. The student claims the coefficient of x is 10. Find k if the claim is correct.
(single)Find k given k + 4 = 10.(3)
18
Stretch question. Expand and simplify fully, then factorise the result where possible: (2x + 3)(x - 4) + (x + 1)(x - 2).
(single)(2x + 3)(x - 4) + (x + 1)(x - 2). Expand, simplify and factorise where possible.(3)
Mark scheme · KS3.M-A13 Expanding Double Brackets

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