Chapter 1: Expressions, Equations & Inequalities
Section 3: Algebraic Expressions
Name ___________________ Date ____________ Period ________
Algebraic Expressions
*If you are absent the day we complete this handout together in class it is your responsibility to fill it in;
please borrow from a friend to get the notes you missed!
 Vocabulary
o Variable – A letter used to represent a number
 Ex. x = 3
 “x” is the variable and the number it represents is 3
 Ex. x + 5 = 7
 “x” is the variable and the number it represents is 2
o Algebraic Expression – contains one or more variables (letters)
 Ex. x – 10
 Ex. 13 + m
 Ex. 10n
 Ex. a + b
o Numerical Expression – Contains numbers, but NOT variables (letters)
 Ex. 8 – 5
 Ex. 3(4 + 1)
 Examples
o Is each expression algebraic or numerical?

7+2

4m + 6

2(5 – 4)
Chapter 1: Expressions, Equations & Inequalities
Section 3: Algebraic Expressions
o
Key Word
Less than
More than
Sum
Difference
Product
Quotient
Operation ( +, −, ×, ÷ )
o What is an algebraic expression for each phrase?

The difference of a number, x, and ½.

12 less than a number, p.
****Note that with subtraction the wording determines the order!

The product of 9 and a number t.

The sum of a number, m, and 7.1.

The quotient of 207 and a number, n.

The sum of the product of a number k and 4, and a number m.

Nine more than the product of a number, x, and two.

The quotient of the sum of 2 and a number, b, and 3.

Jordan currently has $102 and gets and additional $12 per day for doing
chores.
Chapter 1: Expressions, Equations & Inequalities
Section 3: Algebraic Expressions
o Use words to describe each algebraic expression

6n

x
2

p–1

6n – 1
o Evaluate:

g + 2g – g -1 given than g = 2

4x + 7y +3x – 2y + 2x given that x = -3 and y = 2

-h2 – (3h – 5j) + 4j given that h = -1 and j = -4

4(2w – x) – 3(2w – x) given that w = -5 and n = -2

m2 + 100 given than m = √11
Chapter 1: Expressions, Equations & Inequalities
Section 3: Algebraic Expressions
Combining “Like Terms”

Like Term – Must have the same variable (letter) AND the same exponent on the
variable; the coefficient (number in front) does not matter

When terms are “like” they can be combined by keeping the “term” and doing
the math on the coefficient

It is important to remember that “the sign before it goes with it”
o Ex. -4xy2 is a negative (or subtraction) term
o Ex. 6mn3 is a positive (or addition) term
o Example #1: Simplify: 7m2 + 3n -5m2 + 4m
 7m2 and -5m2 are “like terms” because they both contain the
variable “m” and both have an exponent of “2”; 5m2 is negative
since “the sign before it goes with it”
 7m2 – 5m2 = 2m2  this is combining like terms!
 Since 3n and 4m do not have any terms that are “like” they stay
as is and the final answer is 2m2 + 4m + 3n
o Are the terms “like” or “not like”? If “not like,” explain why.
1.
2.
3.
4.
5.
8x3 and 8x2
7xyz and 10xyz
-3mn and -3m2n
4p3q2r and 14p3q2r
h7k and 13hk7
Chapter 1: Expressions, Equations & Inequalities
Section 3: Algebraic Expressions
o Simplify by combining Like Terms:
1. 3x2 + 5x2
2. 4xy3 – x3y
3. -6x4 + 11x4
4. 2x2y4 – 7x2y4
5. 4x – 1 + 5x3 + 7x
6. (x2 – 2x + 3) + (3x2 – 2x – 1)
7. (5x3 – x2 + 6x – 3) + (-2x3 + 4x2 – 2x + 1)
8. (x3 – 3x2 + 5x) – (7x3 + 5x2 – 12)
9. (5r3 + 8) + (6r3 + 3)
10. (x2 – 2) – (3x + 5)
11. –(2a + b) – 2(-a – b)
12. m(3 – n) + n(m + 7)