Simplifying Expressions!
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Name________________________________
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Date___________________ Class ________
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Directions: Write the first step you would use in simplifying the following expressions.
Write it in words and then specifically in symbols. See examples.
Example: 3x + 2x + 5 - 9
!Combining like terms; 5x − 4
Example: 6 − 2(5 − 3x) Distributing; 6 − 10 + 6x
1)
9(2x + 3)
2)
5(3x − 4) − (10 − 7x) + 8x ________________________________________
___________________________________________________________
___________________________________________________________________________
3)
10 + 20 ÷ 5 + 1 _____________________________________________________
4)
3n − 5 + 4(−7 + 2n + 1) + 29 _________________________________________
5)
3(−6n − 5) __________________________________________________________
6)
8(2n + 6) + 2n ______________________________________________________
7)
3x + 4 − 5x _________________________________________________________
8)
5x − 6 + 7 __________________________________________________________
9)
10 2 + 2 − 1 _________________________________________________________
10)
6 + 20 ÷ (4 + 1) − 2 ________________________________________________
11) 9 + 2 ⋅ 6 −
3 _________________________________________________________
12) −(7x − 8) +
13) 2x −
x _______________________________________________________
4 + 6x − (+x) __________________________________________________
14) 5(2x − 9) −
7 ________________________________________________________
15) 15 − 3(4x + 2)
_______________________________________________________
Simplifying Expressions Worksheet
Directions: Decide whether or not the distributive property is used in simplifying the
following expressions. Write yes if it is, no if it is not.
16) 5(2x − 3) ______
19) (3x ⋅ 5) + 6 ______
22) −(4x − 1) ______
17) 8 − 6x(−3x − 4) ______
20) 2x + 3(7 − 2x) ______
23) 8 − 9x + (5x − 12) ______
18) (4x − 1)⋅ 5 ______
21) 1+ (2x − 3) ÷ 4 ______
24) (3x + 5) + 6x ______
Directions: Combine like terms.
25)
9x + 3 + 6x − x 2 − 7 =
26)
−5x − 4 − −10 − +7x + 8x = ______________________________________
27)
10 + 20x 2 + x − 5 + x 2 = ___________________________________________
28)
3n − 5 + 4n + 2n + 1− 2 − 9n = ______________________________________
29)
3a − 4a + −5 − b 2 + 2b = ___________________________________________
30)
8n − 1− 2n + 1+ 10n = ___________________________________________
31)
3x 2 + 4 − 5x 2 + x 2 = ___________________________________________
32)
5.6x − 6.8 + 7.1x − 12x + 4 = _______________________________________
33)
2
1
3 x 2 + 4 − 5 x 2 − −7.2 − x 2 − 6.7 =
_______________________________
5
9
34)
2x 1
5
5
1
− +4 x− x+4 =
3 4
6
8
8 ________________________________________
___________________________________________
Directions: Simplify the following expressions by using the distributive property.
35)
−9(8x − 3) =
36)
−5(−3x − 7) − x(10x 2 − 6x) = ____________________________________
___________________________________________
37)
(10 + 20n)n = ___________________________________________
38)
(3n − 5n 2 + 4)(−7) = ___________________________________________
39)
5 − (−11n − 2) = ___________________________________________
40)
8(2n − 6 + 5n 2 ) = ___________________________________________
Directions: Simplify the following expressions completely.
41)
9(2x + 3) + 6x =
42)
5(3x − 4) − (10 − 7x) + 8x = ______________________________________
43)
10 + 20 ÷ 5 + 1 = ___________________________________________
44)
3n − 5 + 4(−7 + 2n + 1) + 29 = _______________________________________
45)
3(−6n − 5) = ___________________________________________
46)
8(2n + 6) + 2n = ___________________________________________
47)
3x + 4 − 5x + x = ___________________________________________
48)
5x − 6 + 7 − x = ___________________________________________
49)
10 2 + 2 − 1+ (3 + 1)2 = ___________________________________________
50)
6 + 20 ÷ (3 + 1) − 2 = ___________________________________________
51)
−9 + 2 ⋅ 6 − 3 = ___________________________________________
52)
−(7x − 8) + x − 1 = ___________________________________________
53)
2x − 4 + 6x − (+x) + 4 = ___________________________________________
54)
5(2x − 9) − 7 = ___________________________________________
55)
15 − 3(4 x + 2) = ___________________________________________
56)
−6 − x(4 x 2 + 2x − 8) = ___________________________________________
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Try these!
Distribute. Combine like terms afterward if possible. Pick LCM of denominators to multiply by in
problem 60.
57)
⎛ 3x 2 4x ⎞
10 ⎜ − + ⎟ =
⎝ 10 5 2 ⎠
58)
⎛ 2 5n 1 ⎞
6⎜ −
+
=
⎝ 3 6 2 ⎟⎠
59)
1⎞
⎛ 5 x 2
⎜⎝ − − + x − ⎟⎠ (18 ) =
9 6 3
2
60)
( __ ) ⎛⎜⎝
1 2x 3x ⎞
−
+ ⎟=
2 3
4⎠