Math 6A, Lesson 1, Spring 2021, 1/31/2021

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Simplification of Linear Algebraic Expressions

Report card for Fall 2020 was mailed to parents last week.

A 10 minutes quick quiz

1. The distributive law is applicable when removing parentheses in an algebraic expression. Examples in class:

  • 2(3x + 4y) =
  • -4(5a – 3b) + 7a
  • a(2x + 7y + 5z)
  • (2p + 3q -4r)(-6b)
  • 2[x- 5(3-x)]

2. Express each of the following as a single fraction in the simplest form. Recall LCM of denominators.

  • -p + p/3 +(3p)/5
  • (3p + 10)/4 -2
  • (3x – 4)/4 + (2x+5)/3
  • (1 – 2x)/3 + (3x + 1)/5 + (4x -3)/6

3. Home Work:

  • Handout:
    • two pages
  • Workbook: correct last week’s HW problem of
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

Math 6A, Lesson 16, Fall 2020, 1/24/2021

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Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

1. Use of parentheses and distributive law

  • a(x + y) = ax + ay
  • (x + y)a = a(x + y) = ax + ay = xa + xy
  • a(x – y) = a{x + (-y)] = ax + a(-y) = ax – ay
  • a(x + y + z) = ax + ay + az
  • x – (a – b) = a -a + b

2. Addition and subtraction of linear algebraic expressions: explained in class

  • (2a +3b) + (5a -4b) =
  • Find the sum of -2p + 3q – 4 and p + 5q – 3
  • (4x – 5) – (7x – 3)

3. Home Work:

  • Handout:
    • one pages
  • Workbook:
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

Math 6A, Lesson 15, Fall 2020, 1/17/2021

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Like Terms and Unlike Terms

1. Terms, coefficient, and constant terms

  • The expression 2x – 3y + 8 consists of three terms. They are 2x, -3y and 8. The numerical part, including the sign, of a term is called the coefficient of the variable.
  • Term 2x, the coefficient of x is 2
  • Term -3y, the coefficient of y is -3
  • Term 8, is called constant term

2. Classify the like terms and unlike terms: explained in class

3. Simplify the algebraic expression by combining (or collecting) like terms

  • 2x + 3x = 5x
  • 8y – 3y = 5y
  • 3a + 4b – 2a + 5b = (3a -2a) + (4b +5b) = a + 9b

4. Home Work:

  • Handout: two pages
  • Workbook:
    • page 21: 1, 2
    • Page 22: 6, 9, 10

Math 6A, Lesson 14, Fall 2020, 01/10/2021

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1. Exam on chapter 3 “Introduction to Algebra”

2. Home Work: 

  • Redo all the problems you got wrong in last three homework assignment.