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2.01 Simplifying algebraic expressions

Worksheet
Like terms in algebraic expressions
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

For each of the following expressions:

i

State the pairs of like terms.

ii

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
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

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

11 + y

e

9 y+3y-1

f

10 y + 1

5

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

a

9 + 8 r

b

9 r + 8

c

17 r

d

72 r

e

9 r + 8 - r + 1

f

10 r + 2 - 2r + 7

6

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

7

Simplify:

a
2 a + 5 a
b
10 x + 6 x
c
4 b + 3 b
d
12 y - 3 y
e
6 x - 9 x
f
- 5 m - 10 m
g
3 c + 4 c + 7 c
h
-3 n + 6 n + 3 n
i
15 x - 6 x - 2 x
j
19 b - 12 b - 6 b
k
8x - 3x + 7x
l
x + 9 + 7
m
7 x - \left( - 10 x \right) - 8 x
n
- 6 x - 5 x - 3 + 8
o
- 5 p q + \left( - 4 p q \right)
p
4xy+10xy-9xy
q
10ab+3ab-8ba
r
12 n - 9 m - 7 n
s
2 u^{2} + 9 u^{2}
t
- 5 x^{2} - 2 x^{2}
8

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
9

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
10

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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Outcomes

MA.7.AR.1.1

Apply properties of operations to add and subtract linear expressions with rational coefficients.

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