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Warm Up 01/18/17 Simplify. 1. 4 2 2. (–2) 2 3. –(5 y 2 )

Warm Up 01/18/17 Simplify. 1. 4 2 2. (–2) 2 3. –(5 y 2 ). 4. 2(6 xy ). Essential Question. How do you find special products of binomials?. Vocabulary. perfect-square trinomial difference of two squares. F. L. I.

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Warm Up 01/18/17 Simplify. 1. 4 2 2. (–2) 2 3. –(5 y 2 )

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  1. Warm Up 01/18/17 Simplify. 1.42 2. (–2)2 3. –(5y2) 4. 2(6xy)

  2. Essential Question How do you find special products of binomials?

  3. Vocabulary perfect-square trinomial difference of two squares

  4. F L I A trinomial of the form a2 + 2ab + b2 is called a perfect-square trinomial. A perfect-square trinomial is a trinomial that is the result of squaring a binomial. (a + b)2 = (a + b)(a + b) = a2+ ab + ab+ b2 O = a2 + 2ab + b2

  5. Example 1: Finding Products in the Form (a + b)2 A. (x +3)2 (a + b)2 = a2 + 2ab + b2 (x + 3)2 = x2 + 2(x)(3) + 32 = x2 + 6x + 9 B. (4s + 3t)2 (a + b)2 = a2 + 2ab + b2 (4s + 3t)2 = (4s)2 + 2(4s)(3t) + (3t)2 = 16s2 + 24st + 9t2

  6. F L I (a – b)2 = (a – b)(a – b) = a2–ab –ab+ b2 O = a2 – 2ab + b2 A trinomial of the form a2 – ab + b2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b).

  7. Example 2: Finding Products in the Form (a – b)2 A. (x –6)2 (a – b)2 =a2 – 2ab + b2 (x – 6)2 =x2 – 2x(6) +(6)2 = x2 – 12x + 36 B. (4m – 10)2 (a – b)2 =a2 – 2ab + b2 (4m – 10)2 = (4m)2 – 2(4m)(10) + (10)2 = 16m2 – 80m + 100

  8. You can use an area model to see that (a + b)(a–b)= a2 – b2. So (a + b)(a – b) = a2 – b2. A binomial of the form a2 – b2 is called a difference of two squares.

  9. Example 3: Finding Products in the Form (a + b)(a – b) Multiply. A. (x + 4)(x – 4) (a + b)(a –b) =a2 –b2 (x + 4)(x –4) =x2 –42 = x2 – 16 B. (p2 + 8q)(p2 – 8q) (a + b)(a –b) =a2 –b2 (p2 + 8q)(p2–8q) = (p2)2 –(8q)2 = p4 – 64q2

  10. Check It Out! Multiply. c. (9 + r)(9 – r) (a + b)(a –b)=a2 –b2 (9 + r)(9–r)=92 –r2 = 81 – r2

  11. Example 4: Problem-Solving Application Write a polynomial that represents the area of the yard around the pool shown below.

  12. 3 Solve = x2 + 10x + 25 = x2 – 4 Example 4 Continued Step 1 Find the total area. (x +5)2 = x2 + 2(x)(5)+ 52 Use the rule for (a + b)2: a = x and b = 5. Step 2 Find the area of the pool. (x + 2)(x –2) = x2 – 2x + 2x – 4 Use the rule for (a + b)(a – b): a = x and b = 2.

  13. 3 Area of yard total area area of pool Solve – = a – (x2 – 4) x2 + 10x + 25 = Example 4 Continued Step 3 Find the area of the yard around the pool. Identify like terms. = x2+ 10x + 25 – x2 + 4 Group like terms together = (x2 – x2)+ 10x+ ( 25 + 4) = 10x + 29 The area of the yard around the pool is 10x + 29.

  14. Lesson Quiz: Part I Multiply. 1. (x + 7)2 2. (x – 2)2 3. (5x + 2y)2 4. (2x – 9y)2

  15. Lesson Quiz: Part II 5. Write a polynomial that represents the shaded area of the figure below. x + 6 x – 7 x – 6 x – 7

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