Factor completely. 79) d3 1 80) n3 125 81) p3 27 82) g3 8 83) k3 64 84) z3 1000 85) 27m3 125 86) 64c3 1 87) 125y3 8 88) 27a3 64 89) 1000c3 d 3 90) 125v3 w3 91) 8j3 27k3 92) 125m3 27n3 93) 64x3 125y3 94) 27a3 1000b3 95) 6c3 48 96) 9k3 9 97) 7v3 7000w3 98) 216a3 64b3 99) p6 1 100) h6 64 Extend the concepts of this section to factor completely. 101) (x 5)2 (x 2)2 102) (r 6)2 (r 1)2 103) (2p 3)2 (p 4)2 104) (3d 2)2 (d 5)2 105) (t 5)3 8 106) (c 2)3 27 107) (k 9)3 1 108) (y 3)3 125 55) 4t2 25 56) 64z2 9 57) 1 4 k2 4 9 58) 1 36 d2 4 49 59) b4 64 60) u4 49 61) 144m2 n4 62) 64p2 25q4 63) r4 1 64) k4 81 65) 16h4 g4 66) b4 a4 67) 4a2 100 68) 3p2 48 69) 2m2 128 70) 6j 2 6 71) 45r4 5r2 72) 32n5 200n3 Objective 3: Factor the Sum and Difference of Two Cubes 73) Find the following. a) 43 b) 13 c) 103 d) 33 e) 53 f) 23 74) If xn is a perfect cube, then n is divisible by what number? 75) Fill in the blank. a) ( )3 y3 b) ( )3 8c3 c) ( )3 125r3 d) ( )3 x6 76) If xn is a perfect square and a perfect cube, then n is divisible by what number? Complete the factorization. 77) x3 27 (x 3)( ) 78) t3 125 (t 5)( ) R4) Write down four examples of binomials that are differences of two cubes. R5) Why is it that you can factor a sum of two cubes but not a sum of two squares? R6) Which exercises in this section do you fi nd most challenging? R1) How do you know if a trinomial is a perfect square? R2) When does the product of two binomials result in the difference of two squares? R3) Write down four examples of binomials that are differences of two squares. www.mhhe.com/messersmith SECTION 7.3 Special Factoring Techniques 387
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