Sign In | Subscribe
INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
Start learning today, and be successful in your academic & professional career. Start Today!
Loading video...
This is a quick preview of the lesson. For full access, please Log In or Sign up.
For more information, please see full course syllabus of Algebra 1
  • Discussion

  • Study Guides

  • Practice Questions

  • Download Lecture Slides

  • Table of Contents

  • Related Books

Bookmark and Share
Lecture Comments (2)

1 answer

Last reply by: Dr Carleen Eaton
Sat Jan 16, 2016 11:00 PM

Post by Jessie Carrillo on January 14 at 09:02:47 PM

isnt the answer for example II's answer 9p squared - 42pq squared + 49q squared?

Special Products

  • Understand and memorize the following special cases of products: the square of the sum of two terms, the square of the difference of two terms, and the product of the sum and the difference of the same two terms.
  • The first two are called perfect squares and the last one is called the difference of two squares. All of them are important and are used often in later work. Be sure you know this material well.

Special Products

Multiply:
( 3x + 6y )2
  • ( 3x )2 + 2( 3x )( 6y ) + ( 6y )2
9x2 + 36xy + 36y2
Multiply:
( 4g + 7h )2
  • ( 4g )2 + 2( 4g )( 7h ) + ( 7h )2
16g2 + 56gh + 49h2
Multiply:
( 2s − 5t )2
  • ( 2s )2 − 2( 2s )( 5t ) + ( 5t )2
4s2 − 20st + 25t2
Multiply:
( 8x − 11y )2
  • ( 8x )2 − 2( 8x )( 11y ) + ( 11y )2
64x2 − 176xy + 121y2
Multiply:
( 9u + v )2
  • ( 9u )2 − 2( 9u )( v ) + ( v )2
81u2 + 18uv + v2
Multiply:
( 6b − 7c )2
  • ( 6b )2 − 2( 6b )( 7c ) + ( 7c )2
36b2 − 84bc + 49c2
Multiply:
( 7q2 + 4p2 )( 7q2 − 4p2 )
  • a2 − b2
  • a = 7q2
  • b = 4p2
  • ( 7q2 )2 − ( 4p2 )2
49q4 − 16p4
Multiply:
( 2x2 − 3y2 )( 2x2 + 3y2 )
  • ( 2x2 )2 − ( 3y2 )2
4x4 − 9y4
Multiply:
( 5x + 2 )( 5x − 2 )( 5x + 2 )( 5x − 2 )
  • Step One:( 5x + 2 )( 5x − 2 )
  • ( 5x )2 − ( 2 )2
  • 25x2 − 4
  • Step Two:( 25x2 − 4 )( 25x2 − 4 )
  • ( a − b )2 = a2 − 2ab + b2
  • a = 25x2
  • b = 4
  • ( 25x2 )2 − 2( 25x2 )( 4 ) + 42
625x4 − 200x2 + 16
Multiply:
( x + 3 )( x − 3 )( x + 3 )( x − 3 )
  • ( x + 3 )( x − 3 )
  • ( x )2 − ( 3 )2
  • x2 − 9
  • ( x2 − 9 )( x2 − 9 )
  • ( x2 )2 − 2( x2 )( 9 ) + 92
x4 − 18x2 + 81

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Special Products

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Square of a Sum 0:06
    • Example
  • Square of a Difference 2:46
    • Example
  • Difference of Two Squares 4:50
    • Example
  • Example 1: Multiply 6:24
  • Example 2: Multiply 8:34
  • Example 3: Multiply 11:03
  • Example 4: Multiply 12:54