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Australia
Year 7

6.05 Collecting like terms

Worksheet
Like terms
1

State whether the following pairs are like terms:

a

9 y and 10 y

b

2 x y and 4 y x

c

13 u v and 17 v u

d

10 z and 10 b

e

8 y and 5 y

f

5ab and 3cb

g

12mn and 18nm

h

11pr and 22rp

2

State the pairs of like terms in the following expressions:

a
10 m + 2 + 8m + 3
b
9s - r - 6s + 1
c
k + 7j - 5 + 4k
d
10y + 4 + 5x + 3 - y
e
9 + 9a - 7b + 20 - 11a - 15b
f
2a - 3b + 9 - 10c
g
11mn - 15op - 8mn + 22
h
21 - 17ab - 3cd - 5ab + 7cd
Simplify expressions
3

Consider the expression: 4 y - 3 y.

a

Simplify the expression.

b

Explain why the answer to part (a) was not 1 y.

4

For each of the following expressions:

i

State the pairs of like terms.

ii

Hence, simplify the expression.

a
5 u + 7 + 8 u + 8
b
7 u + 2 v - 7 u
c
4x - 6 + 5x
d
12 + 6x + 7y - 8
5

State whether the following expressions are equal to 11y:

a

9 + y + 10 y - 9

b

6 y - 5 y

c

5 y + 6 y

d

10 y + 1

6

State whether the following expressions is equal to 8 r + 9:

a

9 + 8 r

b

17 r

c

9 r + 8 - r + 1

d

10 r + 2 - 2r + 7

7

State whether the following expressions is equal to 9 r t + 8:

a

5 r + 4 t + 8

b

8 + 4 r t + 5 r t

c

9 r + 8 t

d

17 r t

8

Simplify the following by collecting like terms:

a
2 a + 5 a
b
4 b + 3 b
c
4 x + 7 x - 5
d
15 b - 7 b + 10 + 1
e
9 + 7m - 2 + 3m
f
10 x + 12 + 6 x - 7
g
12 y - 3 y + 1
h
3 c + 4 c + 7 c
i
15 x - 6 x - 2 x
j
19 b - 12 b - 6 b
k
-3 n + 6 n + 3 n
l
8x - 3x + 7x
m
4xy+10xy-9xy
n
10ab+3ab-8ba
9

Simplify:

a
10 x - 9 y - 7 x + 11 y
b
11 m + 8 n + 14 m
c
9 x y + 20 + 12 y x -3
d
6 p + 8 q - 6 p
e
8x+9y-5x+10y
f
7a+11a+9b-b
g
8 x + 6 y - 2 y - 4 x + 2 + 3
h
10 m + 7 + 9 n + 5 m + 10 n
i
8x+10 - 7y-6z+10z + 3
j
19a+8b-4c-8a+b
k
2ab-7c+ab+9c
l
12j+ 7 + 9k-7k+11j - 2
m
18x-9y+7x+11y + 11
n
11y-6z+y+6z+12-10
o
13m+2n-8m+10n
p
-3s+6t+9s-4t
10

Simplify:

a
5x-2y+8x+4+6z+3y+4z+2
b
2xy+5yz+4xz+8xy+2xz-3yz + 3
c
20+9x-4y+6y+7x+21
d
9mn-8m-7n+7n+10m+2nm
e
11s+6t+3st-2ts+t+10-4s-5
f
13ab-8bc+6ba-9b+11cb
11

Complete the following statements:

a
2x+⬚ = 8x
b
3y+3+⬚+5 = 8y+8
c
7x - 5x + 10 - ⬚ = 2x + 1
d
9x + 4y + ⬚ = 9x + 6y
e
7x + ⬚ +10y - ⬚ = 11x + 6y
f
8ab + ⬚ + 9b + 6ab = ⬚ + 11b
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Outcomes

ACMNA177

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions

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