Middle Years
6.05 Collecting like terms
Worksheet
1
State whether the following pairs are like terms:
a
9 y and 10 y
b
9 n^{2} and 2 n
c
2 x y and 4 y x
d
10 x^{2} y and 9 y^{2} x
e
6 x^{3} y and 10 y x^{3}
f
13 u v and 17 v u
g
10 z and 10 b
h
8 y and 5 y
2
Simplify the following by collecting like terms:
a
2 a + 5 a
b
10 x + 6 x
c
4 b + 3 b
d
12 y - 3 y
e
3 c + 4 c + 7 c
f
15 x - 6 x - 2 x
g
19 b - 12 b - 6 b
h
-3 n + 6 n + 3 n
i
8x - 3x + 7x
j
20x^2 - 12 x^2 + 10x^2 - x^2
k
4xy+10xy-9xy
l
10ab+3ab-8ba
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
3p + 5p^2 - 3p^2 + p
d
4x - 6 + 5x
5
Simplify:
a
8 x + 6 y - 2 y - 4 x
b
10 m + 9 n + 5 m + 10 n
c
10 x - 9 y - 7 x + 11 y
d
11 m + 8 n + 14 m
e
9 x y + 12 y x
f
6 p + 8 q - 6 p
g
9 p^{2} - 11 p + 11 p^{2}
h
7n^2 + n^2 - 4m + 2m^2 - 5n^2
i
8x+9y-5x+10y
j
7a+11a-9b+b
k
12x^2+10x-9x-5x^2
l
8x-7y-6z+10z
m
15y-8y^2+10y-y^2
n
19a-8b+4c-8a+b
o
2ab-7c+ab+9c
p
12j+9k-7k+11j
q
18x-9y+7x+11y
r
11y-6z+y+6z
s
13m+2n-8m+10n
t
-3s+4t-6t+9s
6
Simplify:
a
5x+2y-8x+6z-3y+4z
b
2xy+5yz+4xz-8xy+2xz-3yz
c
8x^2+10x-6+4x^2-x+11
d
20-9x+4y+6y-7x+21
e
9mn+8m-7n+7n-10m+2mn
f
-6+8x^2-9+5x+16x^2
g
11s+6t+3st-2ts+t-4s
h
13ab-8bc+6ba-9b+11cb
7
Complete the following statements:
a
2x+⬚ = 8x
b
7x - ⬚ = 2x
c
9x + 4y + ⬚ = 9x + 6y
d
7x + ⬚ +10y - ⬚ = 11x + 6y
e
5x^2 - 2x + ⬚ + ⬚ = 9x^2 + 3x
f
8ab + ⬚ + 9b + 6ab = ⬚ + 11b
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