Question 1
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Expanding Double Brackets - Worksheets, Questions and Revision
30 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.
This topic is chapter 10 of KS3 Maths: Algebra Practice Book 1.
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KS3 · Algebra
2.13 Expanding Double Brackets
AQA KS3.M-A13 · Calculators not allowed · about 100 minutes
Name: _______________________________ Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Expand and simplify: (2x - 3)(x2 + 2x - 1).
(single)(2x - 3)(x2 + 2x - 1)(3)
2
Expand and simplify: (x + 5)(x - 5).
(single)(x + 5)(x - 5)(2)
3
Expand and simplify fully: (x + 2)(x - 3) - (x - 1)(x + 5).
(single)(x + 2)(x - 3) - (x - 1)(x + 5)(3)
4
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)
5
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)
6
Expand and simplify: (x + 7)(x - 2).
(single)(x + 7)(x - 2)(3)
7
Expand and simplify: (2x + 3)(2x - 1).
(single)(2x + 3)(2x - 1)(3)
8
Expand and simplify: (3x - 2)2.
(single)(3x - 2)2(3)
9
Expand and simplify: (x + 4)(2x + 5).
(single)(x + 4)(2x + 5)(4)
10
Expand and simplify: (x - 3)(3x + 2).
(single)(x - 3)(3x + 2)(3)
11
Expand and simplify: (4x + 1)(x - 2).
(single)(4x + 1)(x - 2)(3)
12
Expand and simplify: (x + 2)(x2 + x + 3). Note: multiply a binomial by a trinomial.
(single)(x + 2)(x2 + x + 3)(4)
13
Expand each pair of brackets. Write your answer in fully simplified form.
(a)Expand (x + 2)(x + 7).(1)
(b)Expand (3x - 1)(x + 5).(1)
(c)Expand (x - 4)(x - 3).(1)
(d)Expand (2x + 5)(x - 2).(1)
14
Expand and simplify: (3x - 2)(x - 6).
(2)
15
Expand and simplify: (x + 7)(x - 7).
(2)
16
Without expanding fully, state the coefficient of x2 in the expansion of (4x + 3)(2x - 5).
(1)
17
Expand (x - 2)(x - 3).
(1)
18
Expand and simplify: (x - 1)2.
(1)
19
Expand and simplify: (x + 3)(x2 + 2x + 4). Note: multiply a binomial by a trinomial.
(3)
20
Expand and simplify: (3x - 1)(x2 + 3x - 2).
(3)
21
Expand and simplify then collect like terms: (x + 5)(x - 4) + (x - 2)(x + 6).
(3)
22
A rectangle has length (x + 6) m and width (3x - 1) m. Expand and simplify an expression for its area, in m2.
(3)
23
A student expands (x + 5)(x + k) and obtains x2 + (k + 5)x + 5k. The student claims the coefficient of x is 13. Find k if the claim is correct, then state the constant term.
(3)
24
Expand (x + 1)(x + 2).
(1)
25
Expand (x + 4)(x - 1).
(1)
26
Expand and simplify: (x + 8)(x - 3).
(2)
27
Square the binomial and simplify: (x + 9)2.
(2)
28
Expand and simplify: (2x - 5)2.
(2)
29
Expand and simplify: (x + 3)(2x + 7).
(2)
30
Expand and simplify: (x - 5)(4x + 1).
(2)
Mark scheme · 2.13 Expanding Double Brackets
Question 1
- (single) M1 2x multiplied across and -3 multiplied across shown
- (single) M1 terms combined correctly
- (single) A1 2x3 + x2 - 8x + 3 cao
- (single) Answer: 2x3 + x2 - 8x + 3
Question 2
- (single) M1 method: use difference of squares or multiply out
- (single) A1 x2 - 25 cao
- (single) Answer: x2 - 25
Question 3
- (single) M1 each pair expanded correctly
- (single) M1 subtraction applied and like terms combined
- (single) A1 -5x - 1 cao
- (single) Answer: -5x - 1
Question 4
- (single) M1 apply multiplication to find each term
- (single) M1 all terms written out
- (single) M1 like terms combined
- (single) A1 2x2 + 5x - 3 cao
- (single) Answer: 2x2 + 5x - 3
Question 5
- (single) M1 expand to get terms ax*2x, ax*(-b), 2*2x, 2*(-b)
- (single) M1 write expanded polynomial with each term
- (single) M1 collect like terms for x term
- (single) A1 2ax2 + (4 - ab)x - 2b cao for the coefficient part, coefficient is 4 - ab
- (single) Answer: 2ax2 + (4 - ab)x - 2b
Question 6
- (single) M1 two products found correctly, e.g. x*x and x*(-2) or 7*x and 7*(-2) or equivalent
- (single) M1 all four terms written before combining or a correct partial combination
- (single) A1 x2 + 5x - 14 cao
- (single) Answer: x2 + 5x - 14
Question 7
- (single) M1 correct multiplication of first terms and outer/inner terms shown
- (single) M1 all four terms or combined equivalent
- (single) A1 4x2 + 4x - 3 cao
- (single) Answer: 4x2 + 4x - 3
Question 8
- (single) M1 method: (3x - 2)(3x - 2) or use a2 - 2ab + b2
- (single) M1 middle term found correctly
- (single) A1 9x2 - 12x + 4 cao
- (single) Answer: 9x2 - 12x + 4
Question 9
- (single) M1 first and outer/inner/last products attempted correctly
- (single) M1 all four terms written
- (single) M1 like terms combined correctly
- (single) A1 2x2 + 13x + 20 cao
- (single) Answer: 2x2 + 13x + 20
Question 10
- (single) M1 multiplication terms found correctly
- (single) M1 terms combined where appropriate
- (single) A1 3x2 - 7x - 6 cao
- (single) Answer: 3x2 - 7x - 6
Question 11
- (single) M1 multiplications shown correctly
- (single) M1 like terms combined
- (single) A1 4x2 - 7x - 2 cao
- (single) Answer: 4x2 - 7x - 2
Question 12
- (single) M1 x multiplied by each term of the trinomial or equivalent
- (single) M1 2 multiplied by each term of the trinomial or equivalent
- (single) M1 all terms collected
- (single) A1 x3 + 3x2 + 5x + 6 cao
- (single) Answer: x3 + 3x2 + 5x + 6
Question 13
- (a) B1 x2 + 9x + 14 cao
- (a) Answer: x2 + 9x + 14
- (b) B1 3x2 + 14x - 5 cao
- (b) Answer: 3x2 + 14x - 5
- (c) B1 x2 - 7x + 12 cao
- (c) Answer: x2 - 7x + 12
- (d) B1 2x2 + x - 10 cao
- (d) Answer: 2x2 + x - 10
Question 14
- M1 three or four correct terms before collecting
- A1 3x2 - 20x + 12 cao
- Answer: 3x2 - 20x + 12
Question 15
- M1 three or four correct terms before collecting
- A1 x2 - 49 cao
- Answer: x2 - 49
Question 16
- B1 8 cao
- Answer: 8
Question 17
- B1 x2 - 5x + 6 cao
- Answer: x2 - 5x + 6
Question 18
- B1 x2 - 2x + 1 cao
- Answer: x2 - 2x + 1
Question 19
- M1 multiplies the trinomial by x correctly
- M1 multiplies the trinomial by 3 correctly
- A1 x3 + 5x2 + 10x + 12 cao
- Answer: x3 + 5x2 + 10x + 12
Question 20
- M1 multiplies the trinomial by 3x correctly
- M1 multiplies the trinomial by -1 correctly
- A1 3x3 + 8x2 - 9x + 2 cao
- Answer: 3x3 + 8x2 - 9x + 2
Question 21
- M1 expands (x + 5)(x - 4) correctly
- M1 expands (x - 2)(x + 6) correctly
- A1 2x2 + 5x - 32 cao
- Answer: 2x2 + 5x - 32
Question 22
- M1 sets up area as (x + 6)(3x - 1)
- M1 expands correctly before collecting
- A1 3x2 + 17x - 6 cao
- Answer: 3x2 + 17x - 6
Question 23
- M1 forms k + 5 = 13
- A1 k = 8 cao
- B1 constant term = 40 (ft their k)
- Answer: k = 8, constant term = 40
Question 24
- B1 x2 + 3x + 2 cao
- Answer: x2 + 3x + 2
Question 25
- B1 x2 + 3x - 4 cao
- Answer: x2 + 3x - 4
Question 26
- M1 three or four correct terms before collecting
- A1 x2 + 5x - 24 cao
- Answer: x2 + 5x - 24
Question 27
- M1 writes as (x + 9)(x + 9) and expands
- A1 x2 + 18x + 81 cao
- Answer: x2 + 18x + 81
Question 28
- M1 writes as (2x - 5)(2x - 5) and expands
- A1 4x2 - 20x + 25 cao
- Answer: 4x2 - 20x + 25
Question 29
- M1 three or four correct terms before collecting
- A1 2x2 + 13x + 21 cao
- Answer: 2x2 + 13x + 21
Question 30
- M1 three or four correct terms before collecting
- A1 4x2 - 19x - 5 cao
- Answer: 4x2 - 19x - 5
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