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79) 3a3 21a2b 2ab 14b2 (3a2 2b)(a 7b) 80) 8c3 32c2d cd 4d2 (8c2 d)(c 4d) 81) 8u2v2 16u2v 10uv2 20uv 2uv(4u 5)(v 2) 82) 10x2y2 5x2y 60xy2 30xy 5xy(x 6)(2y 1) Mixed Exercises: Objectives 1–4 Factor completely. 83) 3mn 21m 10n 70 (n 7)(3m 10) 84) 4yz 7z 20y 35 (4y 7)(z 5) 85) 16b 24 8(2b 3) 86) 2yz3 14yz2 3z3 21z2 z2(2y 3)(z 7) 87) cd 6c 4d 24 (d 6)(c 4) 88) 5x3 30x2y2 xy 6y3 (x 6y2)(5x2 y) 89) 6a4b 12a4 8a3b 16a3 2a3(3a 4)(b 2) 90) 6x2 48x3 91) 7cd 12 28c 3d 6x2(1 8x) (d 4)(7c 3) 92) 2uv 12u 7v 42 93) dg d g 1 94) 2ab 10a 12b 60 2(a 6)(b 5) 95) x4y2 12x3y3 x3y2(x 12y) 96) 8u2 16uv2 3uv 6v3 (u 2v2)(8u 3v) 97) 4mn 8m 12n 24 4(m 3)(n 2) 98) 5c2 20 5c(c 4) 99) Factor out 2 from 6p2 20p 2. 100) Factor out 5g from 5g3 50g2 25g. (v 6)(2u 7) (g 1)(d 1) 5g(g2 10g 5) 2(3p2 10p 1) Factor completely. You may need to begin by factoring out the GCF fi rst or by rearranging terms. Fill It In Fill in the blanks with either the missing mathematical step or the reason for the given step. 71) 4xy 12x 20y 60 4xy 12x 20y 60 4(xy 3x 5y 15) 4x(y 3) 5(y 3) 4(y 3)(x 5) 72) 2m2n 4m2 18mn 36m 2m2n 4m2 18mn 36m 2m(mn 2m 9n 18) 2mm(n 2) 9(n 2) 2m(n 2)(m 9) Factor out the GCF. Group the terms and factor out the GCF from each group. Take out the binomial factor. Factor out the GCF. Group the terms and factor out the GCF from each group. Take out the binomial factor. 73) 3cd 6c 21d 42 3(c 7)(d 2) 74) 5xy 15x 5y 15 5(x 1)(y 3) 75) 2p2q 10p2 8pq 40p 2p(p 4)(q 5) 76) 3uv2 24uv 3v2 24v 3v(u 1)(v 8) 77) 10st 5s 12t 6 (5s 6)(2t 1) 78) 8pq 12p 10q 15 (4p 5)(2q 3) R1) Do you understand how to factor by grouping? R2) Write down a problem you got wrong or that was diffi cult for you to do. Think about where you made a mistake or why it was hard, then redo the problem without looking at your previous work. R3) How would you explain the process of factoring these expressions to a friend? www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 397


messersmith_power_introductory_algebra_1e_ch4_7_10
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