Section 1: Simplification of Linear Algebraic Expressions

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

Section 2: Factorization by Extracting Common Factors, Factorization by grouping terms

1. The process of writing an algebraic expression as a product of its factors is called factorization or factoring:

• 600 = 2x2x2x3x5x5
• ax + ay = a(x+ y)
• 15a + 20b = 5(3a) + 5(4b)=5(3a + 4b)
• 24ax – 40ay + 8a = (8a)(3x) – (8a)(5y) + (8a)(1) = 8a(3x – 5y + 1)

2. Factorization by grouping

• 12ax – 3ay + 8bx -2by

= (12ax -3ay) + (8bx -2by)

= 3a(4x-y) +2b(4x -y)

=(3a + 2b)(4x-y)

• 49a + 42c -7ay -6cy

= (49a -7ay) + (42c – 6cy)

= 7a(7 – y) + 6c(7 – y)

= (7a + 6c)(7 – y)

3. Home Work:

• Handout:
  • two pages
• Workbook:
  • page 22: 7, 8
  • Page 24: 16, 17, 18, 20
  • Page 26: 26, 27, 28, 29