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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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