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
  • 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
  • Algebraic Expression – contains one or more variables (letters)
  • Ex. x – 10
  • Ex. 13 + m
  • Ex. 10n
  • Ex. a + b
  • Numerical Expression – Contains numbers, but NOT variables (letters)
  • Ex. 8 – 5
  • Ex. 3(4 + 1)
  • Examples
  • Is each expression algebraic or numerical?
  • 7 + 2
  • 4m + 6
  • 2(5 – 4)

Key Word / Operation ( +, −, ×, ÷ )
Less than
More than
Sum
Difference
Product
Quotient
  • 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.
  • Use words to describe each algebraic expression
  • 6n
  • p – 1
  • 6n – 1
  • 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 =

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”
  • Ex. -4xy2 is a negative (or subtraction) term
  • Ex. 6mn3 is a positive (or addition) term
  • 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
  • Are the terms “like” or “not like”? If “not like,” explain why.
  1. 8x3 and 8x2
  2. 7xyz and 10xyz
  3. -3mn and -3m2n
  4. 4p3q2r and 14p3q2r
  5. h7k and 13hk7
  • Simplify by combining Like Terms:
  1. 3x2 + 5x2
  1. 4xy3 – x3y
  1. -6x4 + 11x4
  1. 2x2y4 – 7x2y4
  1. 4x – 1 + 5x3 + 7x
  1. (x2 – 2x + 3) + (3x2 – 2x – 1)
  1. (5x3 – x2 + 6x – 3) + (-2x3 + 4x2 – 2x + 1)
  1. (x3 – 3x2 + 5x) – (7x3 + 5x2 – 12)
  1. (5r3 + 8) + (6r3 + 3)
  1. (x2 – 2) – (3x + 5)
  1. –(2a + b) – 2(-a – b)
  1. m(3 – n) + n(m + 7)