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7-5

7-5. Factoring Special Products. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 1. Holt Algebra 1. Warm Up Determine whether the following are perfect squares. If so, find the square root. 64. yes; 6. 2. 36. 3. 45. 4. x 2. yes; x. 5. y 8. ESSENTIAL QUESTION.

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7-5

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  1. 7-5 Factoring Special Products Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

  2. Warm Up Determine whether the following are perfect squares. If so, find the square root. • 64 yes; 6 2. 36 3. 45 4. x2 yes; x 5. y8

  3. ESSENTIAL QUESTION How do you factor perfect-square trinomials and the difference of two squares?

  4. 3x3x 2(3x8) 88  2(3x 8) ≠ –15x.    9x2– 15x + 64 is not a perfect-square trinomial because –15x ≠ 2(3x  8). Example 1A: Recognizing and Factoring Perfect-Square Trinomials Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2– 15x + 64 9x2– 15x + 64

  5. Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 2 Use the rule. 81x2 + 90x + 25 a = 9x, b = 5 (9x)2 + 2(9x)(5) + 52 Write the trinomial as a2 + 2ab + b2. Write the trinomial as (a + b)2. (9x + 5)2

  6. Example: Recognizing as Perfect-Square Trinomials 36x2– 10x + 14 36x2– 10x + 14 36x2– 10x + 14 is not a perfect-square trinomial.

  7. Factors of 4 Sum  (1 and 4) 5  (2 and 2) 4 Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 1 Factor. x2 + 4x + 4 (x + 2)(x + 2) = (x + 2)2

  8. Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 2 Use the rule. x2 – 14x + 49 a = 1, b = 7 (x)2 – 2(x)(7)+ 72 (x – 7)2 Write the trinomial as (a – b)2.

  9. 3p2– 9q4 3q2 3q2 Example: Recognizing and Factoring the Difference of Two Squares 3p2– 9q4 3p2 is not a perfect square. 3p2– 9q4 is not the difference of two squares because 3p2 is not a perfect square.

  10. 100x2– 4y2 10x 10x 2y 2y   Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 100x2– 4y2 The polynomial is a difference of two squares. a = 10x, b = 2y (10x)2– (2y)2 Write the polynomial as (a + b)(a – b). (10x + 2y)(10x– 2y)

  11. x2 x2 5y3 5y3   Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. x4– 25y6 x4– 25y6 (x2 + 5y3)(x2– 5y3)

  12. 1 1 2x 2x   Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4x2 1 – 4x2 (1 + 2x)(1 – 2x) 1 – 4x2 = (1+ 2x)(1 – 2x)

  13. p4 p4 7q3 7q3 – – Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. p8– 49q6 p8– 49q6 (p4 + 7q3)(p4– 7q3)

  14. 4x 4x Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 16x2– 4y5 16x2– 4y5 4y5 is not a perfect square.

  15. Lesson Quiz: Part I Determine whether each trinomial is a perfect square. If so factor. If not, explain. • 64x2 – 40x + 25 2. 121x2 – 44x + 4 3. 49x2 + 140x + 100

  16. Lesson Quiz: Part II Determine whether the binomial is a difference of two squares. If so, factor. If not, explain. 5. 9x2 – y4 6. 30x2 – y2 7.x2 – y8

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