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Operations with Algebraic Expressions Review Sheet
1. Identify the following properties shown:
a) 9(x + 5) = 9x + 45 ______________________________________________
b) 3 + -3 = 0 ____________________________________________________
c) (1 + 2) + 3 = 1 + (2 + 3) __________________________________________
d) (x + y) + z = (y + x) + z ___________________________________________
e) 7 + 0 = 7 _____________________________________________________
f) 4 
1
 1 _____________________________________________________
4
2.Alex is buying juice for her pre-school class. She knows that she needs a total of 8.5 liters of juice.
However, when she arrives at the grocery store, she sees that the only sell juice in pints.
a) How many pints of juice does Alex need to buy?
b) If there are 4 pints in each bottle of juice, how many bottles of juice should Alex buy to make sure
she has enough for the class?
3. When 4x² + 3x + 2 is subtracted from 2x² – 7x + 5, what is the difference?
4. Multiply and express in standard form:
a) 5(x  3)

b) ( x  2)( x 2  2 x  4)
5.
Given: E = 3.4
F= 2 5
G = 64
H = 7
Which expression represents an integer?
(1) E + G
(2) F + G
(3) G + H
(4) H + E
Which expression does not represent a rational number?
(1) E + G
(2) F + G
(3) G + H
(4) H + E
6. If the sum (2x2 + 7x + 5) + (3x2 – 2x – 6) is multiplied by ½x2, what is the result, written in standard form?
7. Mrs. Connors asked her class “Is the sum of 2.4 and 8 rational or irrational?” Laura answered that the
sum would be irrational. State whether Laura is correct or incorrect. Justify your reasoning.
8. If C = 7x4 – 2x3 + 3x – 2 and D = -x4 + 5x3 + x2 + 4, find:
a) C + D
b) C – D
9. Simplify the following expressions and write all answers using only positive exponents:
a)
 20a 2 b 5
2ab 3
b)
35 x 2 y 6
5 x 3 y 10
10. Simplify:
10 x 2  8 x  2
a)
2
b) (a 2 bc 4 )( a 3b 6 c)
c) (2 x 2 ) 4
d) (3x  8) 2

11. Simplify and express in standard form:
3x2 + 2(5x - 1) + (4x + 9)(3x – 7) + (-6x)2 + 4x
12. Determine if the following statements are always true, sometimes true, or never true.
a) the product of two integers is an integer ________________________________
b) the product of two irrational numbers is irrational _____________________________
c) the sum of two integers is irrational ______________________________
d) the product of two irrational numbers is rational _________________________
e) the sum of two even integers is an even integer _________________________
13. Four expressions are shown below.
I
II
III
IV
10(x2 + 2x – 1)
10(x + 2)(x – 1)
10x(x + 2) – 10
5(2x2 + 4x – 2)
The expression 10x2 +20x – 10 is equivalent to
(1) I and II, only
(3) I, III, and IV
(2) I and IV, only
(4) II, III, and IV