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# 2/27/12 Special Factoring - Sum & Difference of Two Cubes

## by jennoga08 on Feb 26, 2012

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## 2/27/12 Special Factoring - Sum & Difference of Two CubesPresentation Transcript

• Bell Ringer Factor the following: x 2 – 81 x 2 +10x +25 1. 2. Students will be able to factor polynomial equations. Page 356 #3-17
• Today’s Lesson
• Goal : Factor Sum & Differences of Cubes
• Factoring cubes is similar to factoring special cases with quadratics.
• Questions to consider:
• What is a cube?
• How do you think we might factor one?
• What is the purpose of factoring?
• Cubes, Cubes, & More Cubes
• Let’s make a list of cubes!
• Sum & Difference of Cubes
• Sum of Cubes:
• a 3 + b 3 = ( a + b )( a 2 – ab + b 2 )
• Difference of Cubes:
• a 3 – b 3 = ( a – b )( a 2 + ab + b 2 )
• Sum of two Cubes Example
• Factor the following:
• x 3 + 27
• a 3 + b 3 = (a + b)(a 2 – ab + b 2 )
• x 3 + 27 = (x) 3 + (3) 3
• = (x + 3)[(x) 2 − (x)(3) + (3) 2 ]
• = (x + 3)(x 2 − 3x + 9)
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000…
• Difference of two Cubes Example
• Factor the following:
• x 3 - 64
• a 3 – b 3 = ( a – b )( a 2 + ab + b 2 )
• x 3 - 64 = (x) 3 - (4) 3
• = (x - 4)[(x) 2 + (x)(4) + (4) 2 ]
• = (x - 4)(x 2 +4x + 16)
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000…
• Exercises
• x 3 – 125
• x 3 + 216
• Exercises
• 8x 3 – 1
• 27x 3 +343
• Factor a Common Monomial
• Take out our greatest common factor!
• Our goal is to “factor the polynomial completely.”
• Example :
• 3x 4 +9x 2 – 6x
• = 3x(x 3 +3x – 2)
• Factoring a Common Monomial Exercises
• 3x 3 + 9x 2 – 81
• 4x 4 - 16x 3 + 16x 2
• 2x 5 – 18x 3
• Homework
• Page 356
• #3-17
• Sum or Difference of Cubes
• Monomial Factors