7 8 Special Products of Binomials Graph the
7 -8 Special Products of Binomials Graph the system of linear inequalities. y≤ 3 y > –x + 5 Holt Algebra 1
7 -8 Special Products of Binomials Objective Find special products of binomials. Holt Algebra 1
7 -8 Special Products of Binomials Imagine a square with sides of length (a + b): The area of this square is (a + b) or (a + b)2. The area of this square can also be found by adding the areas of the smaller squares and the rectangles inside. The sum of the areas inside is a 2 + ab + b 2. Holt Algebra 1
7 -8 Special Products of Binomials This means that (a + b)2 = a 2+ 2 ab + b 2. You can use the FOIL method to verify this: F L (a + b)2 = (a + b) = a 2 + ab + b 2 I = a 2 + 2 ab + b 2 O 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. Holt Algebra 1
7 -8 Special Products of Binomials Multiply. A. (x +3)2 = (a + b)2 = a 2 + 2 ab + b 2 2 x + 6 x + 9 B. (4 s + 3 t)2 = 16 s 2 + 24 st + 9 t 2 Holt Algebra 1
7 -8 Special Products of Binomials Multiply. C. (5 + m 2)2 = 25 + Holt Algebra 1 (a + b)2 = a 2 + 2 ab + b 2 2 10 m + 4 m
7 -8 Special Products of Binomials Multiply. A. (x + 6)2 (a + b)2 = a 2 + 2 ab + b 2 = x 2 + 12 x + 36 B. (5 a + b)2 = 25 a 2 + 10 ab + b 2 Holt Algebra 1
7 -8 Special Products of Binomials Multiply. (1 + c 3)2 =1+ Holt Algebra 1 (a + b)2 = a 2 + 2 ab + b 2 3 2 c + 6 c
7 -8 Special Products of Binomials You can use the FOIL method to find products in the form of (a – b)2. 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 – 2 ab + b 2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b). Holt Algebra 1
7 -8 Special Products of Binomials Multiply. A. (x – 6)2 (a – b)2 = a 2 – 2 ab + b 2 = x – 12 x + 36 B. (4 m – 10)2 = Holt Algebra 1 2 16 m – 80 m + 100
7 -8 Special Products of Binomials Multiply. C. (2 x – 5 y )2 (a – b) = a 2 – 2 ab + b 2 = 4 x 2 – 20 xy +25 y 2 D. (7 – r 3)2 = 49 – 14 r 3 + r 6 Holt Algebra 1
7 -8 Special Products of Binomials You can use an area model to see that (a + b)(a - b) = a 2 – b 2. The new arrange. Then remove the ment is a rectangle smaller rectangle with length a + b and on the bottom. Turn it and slide it width a – b. Its area is (a + b)(a – b). up next to the top rectangle. 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. Begin with a square with area a 2. Remove a square with area b 2. The area of the new figure is a 2 – b 2. Holt Algebra 1
7 -8 Special Products of Binomials Multiply. A. (x + 4)(x – 4) = 2 x (a + b)(a – b) = a 2 – b 2 – 16 B. (p 2 + 8 q)(p 2 – 8 q) = p 4 – 64 q 2 Holt Algebra 1
7 -8 Special Products of Binomials Multiply. C. (10 + b)(10 – b) (a + b)(a – b) = a 2 – b 2 = 100 – Holt Algebra 1 2 b
7 -8 Special Products of Binomials Multiply. a. (x + 8)(x – 8) = 2 x – 64 b. (3 + 2 y 2)(3 – 2 y 2) =9– Holt Algebra 1 4 4 y
7 -8 Special Products of Binomials Multiply. c. (9 + r)(9 – r) = 81 – Holt Algebra 1 2 r
7 -8 Special Products of Binomials Write a polynomial that represents the area of the yard around the pool shown below. (a + b)2 = a 2 + 2 ab + b 2 (a + b)(a – b) = a 2 – b 2 = 2 x + 10 x + 25 – 2 (x = 10 x + 29 Holt Algebra 1 – 4)
7 -8 Special Products of Binomials Write an expression that represents the area of the swimming pool. 25 – 25 Holt Algebra 1 2 x + 2 x
7 -8 Special Products of Binomials Holt Algebra 1
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