CHAPTER_ppt_6_5 - a 3 b 3 = a b a 2 – ab b 2 a 3 – b 3...

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§ 6.5 Factoring Binomials
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Difference of Two Squares Another shortcut for factoring a trinomial is when we want to factor the difference of two squares. a 2 b 2 = ( a + b )( a b ) A binomial is the difference of two squares if 1.both terms are squares and 2.the signs of the terms are different. 9 x 2 – 25 y 2 c 4 + d 4
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Difference of Two Squares Factor the polynomial x 2 – 9. The first term is a square and the last term, 9, can be written as 3 2 . The signs of each term are different, so we have the difference of two squares Therefore x 2 – 9 = ( x – 3)( x + 3) . Note: You can use FOIL method to verify that the factorization for the polynomial is accurate. Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 There are two additional types of binomials that can be factored easily by remembering a formula. We have not studied these special products previously, as they involve cubes of terms, rather than just squares.
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Unformatted text preview: a 3 + b 3 = ( a + b )( a 2 – ab + b 2 ) a 3 – b 3 = ( a – b )( a 2 + ab + b 2 ) Sum or Difference of Two Cubes Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Factor x 3 + 1. Since this polynomial can be written as x 3 + 1 3 , x 3 + 1 = ( x + 1)( x 2 – x + 1). Factor y 3 – 64. Since this polynomial can be written as y 3 – 4 3 , y 3 – 64 = ( y – 4)( y 2 + 4 y + 16). Sum or Difference of Two Cubes Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 Factor 8 t 3 + s 6 . Since this polynomial can be written as (2 t ) 3 + ( s 2 ) 3 , 8 t 3 + s 6 = (2 t + s 2 )((2 t ) 2 – (2 t )( s 2 ) + ( s 2 ) 2 ) = (2 t + s 2 )(4 t 2 – 2 s 2 t + s 4 ). Factor x 3 y 6 – 27 z 3 . Since this polynomial can be written as ( xy 2 ) 3 – (3 z ) 3 , x 3 y 6 – 27 z 3 = ( xy 2 – 3 z )(( xy 2 ) 2 + (3 z )( xy 2 ) + (3 z ) 2 ) = ( xy 2 – 3 z )( x 2 y 4 + 3 xy 2 z + 9 z 2 ). Sum or Difference of Two Cubes Example:...
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This note was uploaded on 11/04/2011 for the course MATH 103 taught by Professor Alraban during the Fall '10 term at Montgomery College.

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CHAPTER_ppt_6_5 - a 3 b 3 = a b a 2 – ab b 2 a 3 – b 3...

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