6 6 Special Products of Binomials Warm Up

6 -6 Special Products of Binomials Warm Up Simplify. 1. 42 2. (– 2)2 3. –(5 y 2) 4. 2(6 xy) Holt Mc. Dougal Algebra 1 01/18/17

6 -6 Special Products of Binomials Essential Question How do you find special products of binomials? Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Vocabulary perfect-square trinomial difference of two squares Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials A trinomial of the form a 2 + 2 ab + b 2 is called a perfect-square trinomial. A perfect-square trinomial is a trinomial that is the result of squaring a binomial. F L (a + b)2 = (a + b) = a 2 + ab + b 2 I O = a 2 + 2 ab + b 2 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 1: Finding Products in the Form (a + b)2 A. (x +3)2 (a + b)2 = a 2 + 2 ab + b 2 (x + 3)2 = x 2 + 2(x)(3) + 32 = x 2 + 6 x + 9 B. (4 s + 3 t)2 (a + b)2 = a 2 + 2 ab + b 2 (4 s + 3 t)2 = (4 s)2 + 2(4 s)(3 t) + (3 t)2 = 16 s 2 + 24 st + 9 t 2 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials F L (a – b)2 = (a – b) = a 2 – ab + b 2 I O = a 2 – 2 ab + b 2 A trinomial of the form a 2 – ab + b 2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b). Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 2: Finding Products in the Form (a – b)2 A. (x – 6)2 (a – b)2 = a 2 – 2 ab + b 2 (x – 6)2 = x 2 – 2 x(6) + (6)2 = x 2 – 12 x + 36 B. (4 m – 10)2 (a – b)2 = a 2 – 2 ab + b 2 (4 m – 10)2 = (4 m)2 – 2(4 m)(10) + (10)2 = 16 m 2 – 80 m + 100 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials You can use an area model to see that (a + b)(a–b)= a 2 – b 2. So (a + b)(a – b) = a 2 – b 2. A binomial of the form a 2 – b 2 is called a difference of two squares. Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 3: Finding Products in the Form (a + b)(a – b) Multiply. A. (x + 4)(x – 4) (a + b)(a – b) = a 2 – b 2 (x + 4)(x – 4) = x 2 – 42 = x 2 – 16 B. (p 2 + 8 q)(p 2 – 8 q) (a + b)(a – b) = a 2 – b 2 (p 2 + 8 q)(p 2 – 8 q) = (p 2)2 – (8 q)2 = p 4 – 64 q 2 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Check It Out! Multiply. c. (9 + r)(9 – r) (a + b)(a – b) = a 2 – b 2 (9 + r)(9 – r) = 92 – r 2 = 81 – r 2 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 4: Problem-Solving Application Write a polynomial that represents the area of the yard around the pool shown below. Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 4 Continued 3 Solve Step 1 Find the total area. (x +5)2 = x 2 + 2(x)(5) + 52 = x 2 + 10 x + 25 Use the rule for (a + b)2: a = x and b = 5. Step 2 Find the area of the pool. (x + 2)(x – 2) = x 2 – 2 x + 2 x – 4 Use the rule for (a + b)(a – b): a = x 2 – 4 and b = 2. Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Example 4 Continued 3 Solve Step 3 Find the area of the yard around the pool. Area of yard = a total area – area of pool = x 2 + 10 x + 25 – (x 2 – 4) Identify like = + 10 x + 25 – +4 terms. = (x 2 – x 2) + 10 x + ( 25 + 4) Group like terms = 10 x + 29 together x 2 The area of the yard around the pool is 10 x + 29. Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials Lesson Quiz: Part I Multiply. 1. (x + 7)2 2. (x – 2)2 3. (5 x + 2 y)2 4. (2 x – 9 y)2 Holt Mc. Dougal Algebra 1

6 -6 Special Products of Binomials 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 Holt Mc. Dougal Algebra 1