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Simplifying and Collecting Like Terms - Worksheets, Questions and Revision

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This topic is chapter 2 of KS3 Maths: Algebra Practice Book 1.

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KS3 · Algebra

2.5 Simplifying and Collecting Like Terms

AQA KS3.M-A5 · Calculators not allowed · about 95 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Simplify fully by collecting like terms and performing simple multiplications.
(a)Simplify 2(3x) + 4x(3)
2
Simplify and collect like terms after expanding. Show your method.
(a)Simplify 2(x + 3) + x(2)
3
Collect like terms and simplify each expression with two different variables.
(a)Simplify 4x + 3y + 2x - y(3)
4
Simplify each expression that mixes multiplication and addition.
(a)Simplify 4( x + 1 ) + 2x(3)
5
Collect like terms and simplify. Some coefficients are negative.
(a)Simplify -2x + 5x - 3 + 7(3)
6
Simplify and write in simplest form. Combine like terms and simplify products.
(a)Simplify 2( x + 2 ) + 3( x - 1 )(3)
7
Stretch question. Simplify fully, showing each step clearly.
(a)Simplify 3(x + 2) - 2(x - 1) + x(3)
8
Collect like terms and simplify each expression.
(a)Simplify 2x + 5x(1)
(b)Simplify 6y - 2y(1)
(c)Simplify 3a + 4b + 2a(1)
9
Simplify each single-term combination.
(a)Simplify -2m + 7m(1)
(b)Simplify 4p - 9p(1)
(c)Simplify 0 + 6t(1)
10
Simplify each expression by collecting like terms. Show working.
(a)Simplify 8x + 3x - 5x(2)
(b)Simplify 2a + 4b + 3a - b(2)
11
Simplify the expressions and write the result in simplest form.
(a)Simplify 3x + 2 - x + 5(2)
(b)Simplify 6y - 2 + y + 8(2)
12
Simplify each product by multiplying the coefficient only (variables stay as letters).
(a)Calculate 4 x 3x(1)
(b)Calculate -2 x 5y(1)
13
Simplify each quotient by dividing the coefficient only. Keep variables unchanged.
(a)Simplify (12x) ÷ 3(1)
(b)Simplify (9y) ÷ 3(1)
(c)Simplify (-6a) ÷ 2(1)
14
State whether 4x and 4y are like terms. Give your answer as yes or no.
(1)
15
Expand and simplify 6(3y).
(2)
16
Simplify fully: 5x + 3y - 2x + y.
(2)
17
Simplify -3a + 7a.
(2)
18
Expand and simplify 2(x + 5).
(2)
19
Expand and simplify 3(x + 4) + 2x.
(3)
20
Simplify fully: 4a + 3b - a + 5b - 2a.
(3)
21
Expand and simplify 5(2x - 3) - 4x.
(3)
22
Expand and simplify 3(x + 2) + 2(x - 5).
(4)
23
Simplify fully 4(2x - 1) - 3(x - 2), then find its value when x = 3.
(4)
24
State whether 3p and 8p are like terms. Give your answer as yes or no.
(1)
25
Simplify 5x + 2x.
(1)
26
Simplify 9y - 4y.
(1)
27
Simplify 10b / 5.
(1)
28
Simplify 6c + c.
(1)
29
Simplify 8x + 3x - 5x.
(2)
30
Simplify 7a - 2a + 3a.
(2)
Mark scheme · 2.5 Simplifying and Collecting Like Terms

Question 1

  • (a) M1 multiply inside brackets: 2(3x) -> 6x
  • (a) M1 collect like terms: 6x + 4x -> (6+4)x
  • (a) A1 10x cao
  • (a) Answer: 10x

Question 2

  • (a) M1 expand 2(x+3) -> 2x + 6 and then collect with + x
  • (a) A1 3x + 6 cao
  • (a) Answer: 3x + 6

Question 3

  • (a) M1 collect x terms: 4x + 2x and y terms: 3y - y
  • (a) M1 compute: 6x and 2y
  • (a) A1 6x + 2y cao
  • (a) Answer: 6x + 2y

Question 4

  • (a) M1 expand 4(x+1) -> 4x + 4
  • (a) M1 collect like terms 4x + 2x
  • (a) A1 6x + 4 cao
  • (a) Answer: 6x + 4

Question 5

  • (a) M1 collect x terms and constant terms separately
  • (a) M1 compute -2x + 5x = 3x and -3 + 7 = 4
  • (a) A1 3x + 4 cao
  • (a) Answer: 3x + 4

Question 6

  • (a) M1 expand both brackets: 2x+4 and 3x-3
  • (a) M1 collect like terms: 2x + 3x and 4 - 3
  • (a) A1 5x + 1 cao
  • (a) Answer: 5x + 1

Question 7

  • (a) M1 expand brackets: 3x+6 and -2x+2
  • (a) M1 collect like x terms: 3x - 2x + x
  • (a) A1 2x + 8 cao
  • (a) Answer: 2x + 8

Question 8

  • (a) B1 7x cao
  • (a) Answer: 7x
  • (b) B1 4y cao
  • (b) Answer: 4y
  • (c) B1 5a + 4b cao
  • (c) Answer: 5a + 4b

Question 9

  • (a) B1 5m cao
  • (a) Answer: 5m
  • (b) B1 -5p cao
  • (b) Answer: -5p
  • (c) B1 6t cao
  • (c) Answer: 6t

Question 10

  • (a) M1 collecting like terms: 8x + 3x - 5x -> (8+3-5)x
  • (a) A1 6x cao
  • (a) Answer: 6x
  • (b) M1 grouping a terms and b terms: 2a+3a and 4b-b
  • (b) A1 5a + 3b cao
  • (b) Answer: 5a + 3b

Question 11

  • (a) M1 collect like x terms and constants
  • (a) A1 2x + 7 cao
  • (a) Answer: 2x + 7
  • (b) M1 collect like y terms and constants
  • (b) A1 7y + 6 cao
  • (b) Answer: 7y + 6

Question 12

  • (a) B1 12x cao
  • (a) Answer: 12x
  • (b) B1 -10y cao
  • (b) Answer: -10y

Question 13

  • (a) B1 4x cao
  • (a) Answer: 4x
  • (b) B1 3y cao
  • (b) Answer: 3y
  • (c) B1 -3a cao
  • (c) Answer: -3a

Question 14

  • B1 No, because the letters are different
  • Answer: No

Question 15

  • M1 multiplies the coefficients correctly, keeping the variable unchanged
  • A1 18y cao
  • Answer: 18y

Question 16

  • M1 collects the x terms correctly, e.g. 5x - 2x = 3x
  • A1 3x + 4y cao
  • Answer: 3x + 4y

Question 17

  • M1 collects the like terms correctly, keeping track of the negative sign
  • A1 4a cao
  • Answer: 4a

Question 18

  • M1 expands the bracket correctly, e.g. 2x + 10
  • A1 2x + 10 cao
  • Answer: 2x + 10

Question 19

  • M1 expands the bracket correctly, e.g. 3x + 12
  • M1 collects the x terms correctly, e.g. 3x + 2x = 5x
  • A1 5x + 12 cao
  • Answer: 5x + 12

Question 20

  • M1 collects the a terms correctly, e.g. 4a - a - 2a = a
  • M1 collects the b terms correctly, e.g. 3b + 5b = 8b
  • A1 a + 8b cao
  • Answer: a + 8b

Question 21

  • M1 expands the bracket correctly, e.g. 10x - 15
  • M1 collects the x terms correctly, e.g. 10x - 4x = 6x
  • A1 6x - 15 cao
  • Answer: 6x - 15

Question 22

  • M1 expands the first bracket correctly, e.g. 3x + 6
  • M1 expands the second bracket correctly, e.g. 2x - 10
  • M1 collects all like terms correctly
  • A1 5x - 4 cao
  • Answer: 5x - 4

Question 23

  • M1 expands the first bracket correctly, e.g. 8x - 4
  • M1 expands the second bracket correctly, keeping the sign, e.g. -3x + 6
  • A1 5x + 2 cao
  • A1 17 cao when x = 3
  • Answer: 5x + 2; when x = 3 the value is 17

Question 24

  • B1 Yes, because both terms have the letter p
  • Answer: Yes

Question 25

  • B1 7x cao
  • Answer: 7x

Question 26

  • B1 5y cao
  • Answer: 5y

Question 27

  • B1 2b cao
  • Answer: 2b

Question 28

  • B1 7c cao
  • Answer: 7c

Question 29

  • M1 collects the like terms correctly
  • A1 6x cao
  • Answer: 6x

Question 30

  • M1 collects the like terms correctly
  • A1 8a cao
  • Answer: 8a

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