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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Lecture Comments (5)

1 answer

Last reply by: Dr Carleen Eaton
Sat Jun 22, 2013 11:21 AM

Post by Taylor Wright on June 21, 2013

At 18:44

How did you get 3x^6 - 48x^2 = 3x^6 = 48x^2 - 48x^2 ???

where did the extra " = " sign come from?

1 answer

Last reply by: Dr Carleen Eaton
Sat Jun 22, 2013 11:19 AM

Post by Taylor Wright on June 21, 2013

At 1:20

x^2 = (x+4)(x-4) ???

0 answers

Post by Santhini Dheenathayalan on February 7, 2011

This is a very helpful video!!

Factoring the Difference of Two Squares

  • The special rule for factoring the difference of two squares is a2 – b2 = (a + b)(a – b).
  • Sometimes, this rule needs to be applied more than once to completely factor the original polynomial.
  • Some polynomials require several methods to be factored completely. Always start by finding the Greatest Common Factor. Then try other methods.
  • You can solve some quadratic equations by factoring the trinomial and then using the zero product property.

Factoring the Difference of Two Squares

Factor:
25x2 − 64
  • 25x2 = a2
  • a = 5x
  • 64 = b2
  • b = 8
( 5x + 8 )( 5x − 8 )
Factor:
81y2 − 121
  • a2 = 81y2
  • a = 9y
  • b2 = 121
  • b = 11
( 9y + 11 )( 9y − 11 )
Factor:
49t2 − 225
  • a2 = 49t2
  • a = 7t
  • b2 = 15
( 7t + 15 )( 7t − 15 )
Factor:
3m4 − 27m2
  • 3m2( m2 − 9 )
  • a2 = m2
  • a = m
  • b2 = 9
  • b = 3
3m2( m + 3 )( m − 3 )
Factor:
72k4 − 288k2
  • 2k2( 36k2 − 144 )
  • a2 = 36k2
  • a = 6k
  • b2 = 144
  • b = 12
2k2( 6k + 12 )( 6k − 12 )
Factor:
12p4 − 75p2
  • 3p2( 4p2 − 25 )
  • a2 = 4p2
  • a = 2p
  • b2 = 25
b = 5
Factor:
6n4 − 18n3 − 10n2 + 30n
  • 2n(3n3 − 9n2 − 5n + 15)
  • 2n[ ( 3n3 − 9n ) + ( − 5n + 15 ) ]
  • 2n[ 3n2( n − 3 ) − 5( n − 3 ) ]
2n[ ( 3n2 − 5 )( n − 3 ) ]
Factor:
48x4 + 96x3 − 75x2 − 150x
  • 3x( 16x3 + 32x2 − 25x − 50 )
  • 3x[ ( 16x3 + 32x2 ) + ( − 25x − 50 ) ]
  • 3x[ 16x3( x + 2 ) − 25( x + 2 ) ]
  • 3x[ ( 16x2 − 25 )( x + 2 ) ]
3x[ ( 4x + 5 )( 4x − 5 )( x + 2 ) ]
Factor:
5y4 − 34y3 − 20y2 − 35y
  • 5y( y3 − 7y − 4y − 7 )
  • 5y[ ( y3 − 7y2 ) + ( − 4y − 7 ) ]
  • 5y[ y2( y − 7 ) − 4( y − 7 ) ]
  • 5y[ ( y2 − 4 )( y − 7 ) ]
5y[ ( y + 2 )( y − 2 )( y − 7 ) ]
Solve:
4x6 = 324x2
  • 4x6 − 324x2 = 0
  • 4x2( x4 − 81 ) = 0
  • 4x2( x2 + 9 )( x2 − 9 ) = 0
  • 4x2( x2 + 9 )( x + 3 )( x − 3 ) = 0
  • 4x2 = 0x = 0
  • x2 + 9 = 0x2 = − 9√{x2} = √{ − 9} (No Solution)
  • x + 3 = 0x = − 3
  • x − 3 = 0x = 3
x = { 0, − 3,3}

*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

Factoring the Difference of Two Squares

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
  • Difference of Two Squares 0:08
    • Example
  • Factoring Using Several Techniques 2:23
    • Factoring the GCF
    • Example
  • Solving Equations 5:24
    • Example
  • Example 1: Factor the Polynomial 7:34
  • Example 2: Factor the Polynomial 9:11
  • Example 3: Factor the Polynomial 12:00
  • Example 4: Solve the Polynomial 18:31