MATH 1010-005: Intermediate Algebra
Worksheet 2: Algebraic Expressions
1. Identify the terms and constant terms in the following expressions:
(a) 10x+ 4
(b) 6x2+ 4xy โ7
(c) x3
โ4z+ 12w
2. Simplify the following expressions:
(a) x3
โ3x+ 4xโ1
(b) 12xy2+ 3x2yโ4xy โ9xy2
3. Simplify the following expressions using the distributive law:
(a) 7(xโ3) + 3(2x+ 4)
(b) (x+ 2)(xโ4)
(c) (xโ1)(x2+x+ 1)
(d) (x+ 1)(xโ1)(x+ 2)
4. Thanks to the the success of their new ED-209 line of lawnmowers, Omni Consumer Products
(OCP) have raised their dividend payments per share to $0.55 per share. Suppose they have
also paid you $1000 to keep quiet about the problems with the ED-209 program.
(a) Write an algebraic expression describing the amount of money you will receive from OCP
this year.
(b) If you have 10,000 shares of OCP stock, how much money will you receive this year?
5. Lizards have two eyes and tuataras have three (two normal eyes and one parietal eye in the
back of their head).
(a) Write an algebraic expression describing the number of eyes in your terrarium in terms
of the number of lizards and tuataras.
(b) If you have six tuataras and four lizards, how many eyes do you have in your terrarium?
(c) If you have ten eyes in your terrarium, how many lizards and how many tuataras do you
have? (There is more than one answer!)
6. Suppose that when there is an election in Italy, Prime Minister Silvio Berlusconi has 20 points
of support. His support increases by 10% for each media company he controls.
(a) Given that he controlls a single additional media company as prime minister, write an
algebraic expression describing his support given the number of media companies he
owns.
(b) How many media companies does he need to own to win the election?
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