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Factoring Special Products 6.4 1.Factor perfect square trinomials. 2.Factor a difference of squares. 3.Factor a difference of cubes. 4.Factor a sum of cubes.

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Write as many perfect squares as you can. Write as many perfect cubes as you can. 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 625 1 8 27 64 125

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Perfect Square Trinomials: 6x is double the product. -12xy is double the product. Perfect squares

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Perfect Square Trinomials: 15x is not double the product. Caution: Don’t just check the first and last terms!

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Factor completely : -20ab is double the product. Check by foiling! Perfect squares

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Factor completely : -208a is double the product. Check by foiling! Perfect squares

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Factor completely : 24m is double the product. Check by foiling!

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Factor completely : 6 is NOT double the product. Prime Not a perfect square trinomial. It may still be factorable.

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Factor completely :

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Factoring Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2

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Difference of Squares: Conjugates

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Factor completely : Think Conjugates! Check by foiling!

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Factor: Think Conjugates Check by foiling!

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Factor completely : Prime The sum of squares CANNOT be factored!

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Factor completely : Check by foiling!

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Factor completely: Check by foiling!

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Copyright © 2011 Pearson Education, Inc. Factoring a Difference of Squares a 2 – b 2 = (a + b)(a – b) Warning: A sum of squares a 2 + b 2 is prime and cannot be factored.

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Sum and Difference of Cubes Multiply: Same. Cube Root Opposite. SquareProductSquare Always positive 3 terms – trinomial rather than binomial Cube Root

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Factor completely: Cubes = trinomial SquareProductSquare

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Factor completely: Cubes = trinomial SquareProductSquare

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Factor completely: Cubes = trinomial SquareProductSquare

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Copyright © 2011 Pearson Education, Inc. Factoring a Sum or Difference of Cubes a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) a 3 + b 3 = (a + b)(a 2 – ab + b 2 )

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Slide 6- 23 Copyright © 2011 Pearson Education, Inc. Factor completely. 9x 2 – 49 a) (3x + 5) 2 b) (3x + 7)(3x – 7) c) (3x – 7) 2 d) (7x + 3)(7x – 3) 6.4

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Slide 6- 24 Copyright © 2011 Pearson Education, Inc. Factor completely. 9x 2 – 49 a) (3x + 5) 2 b) (3x + 7)(3x – 7) c) (3x – 7) 2 d) (7x + 3)(7x – 3) 6.4

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Slide 6- 25 Copyright © 2011 Pearson Education, Inc. Factor completely. 4a 2 – 20a + 25 a) (2a + 5) 2 b) (2a – 5) 2 c) (4a + 5) 2 d) (4a – 5) 2 6.4

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Slide 6- 26 Copyright © 2011 Pearson Education, Inc. Factor completely. 4a 2 – 20a + 25 a) (2a + 5) 2 b) (2a – 5) 2 c) (4a + 5) 2 d) (4a – 5) 2 6.4

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Slide 6- 27 Copyright © 2011 Pearson Education, Inc. Factor completely. 2n 2 + 24n + 72 a) 2(n + 6) 2 b) 2(n + 6)(n – 6) c) 2(n – 6) 2 d) (2n + 6)(2n – 6) 6.4

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Slide 6- 28 Copyright © 2011 Pearson Education, Inc. Factor completely. 2n 2 + 24n + 72 a) 2(n + 6) 2 b) 2(n + 6)(n – 6) c) 2(n – 6) 2 d) (2n + 6)(2n – 6) 6.4

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