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So, a x2 and b 9. x4 81 (x2 9)(x2 9) Can we factor again? x2 9 is the sum of two squares. It will not factor. x2 9 is the difference of two squares, so it will factor. x2 9 x2 9 (x 3)(x 3) (x)2 (3)2 a x and b 3 Therefore, x4 81 (x2 9)(x2 9) (x2 9)(x 3)(x 3) YOU TRY 3 Factor completely. a) 125d 5d 3 b) 3r2 48 c) z4 1 Summary Special Factoring Rules Perfect square trinomials: a2 2ab b2 (a b)2 a2 2ab b2 (a b)2 Difference of two squares: a2 b2 (a b)(a b) ANSWERS TO YOU TRY EXERCISES 1) a) (g 7)2 b) 6y(y 3)2 c) (5v 1)2 d) (3b 4)(3b 1) 2) a) (m 10)(m 10) b) (2c 9d )(2c 9d) c) ah 8 5 bah 8 5 b d) prime 3) a) 5d(5 d )(5 d) b) 3(r2 16) c) (z2 1)(z 1)(z 1) 7.4 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Factor a Perfect Square Trinomial 1) Find the following. a) 72 49 b) 92 81 c) 62 36 d) 102 100 e) 52 25 f) 42 16 g) 112 121 h) a1 3 b 2 1 9 i) a3 8 b 2 9 64 2) What is perfect square trinomial? It is a trinomial that results from squaring a binomial. 3) Fill in the blank with a term that has a positive coeffi cient. a) (__)2 c4 c2 b) (__)2 9r2 3r c) (__)2 81p2 9p d) (__)2 36m4 6m2 e) (__)2 1 4 1 2 f) (__)2 144 25 12 5 4) If xn is a perfect square, then n is divisible by what number? 2 5) What perfect square trinomial factors to ( y 6)2? 6) What perfect square trinomial factors to (3k 8)2? y2 12y 36 9k2 48k 64 418 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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