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**Sample text**

1–2: If x < 0 and y > 0, determine the sign of the real number. 1 (a) xy (b) x y x ϩx (c) y x y (b) xy 2 (c) 2 (a) 2 (d) y Ϫ x xϪy xy (d) y͑ y Ϫ x͒ Exer. 3–6: Replace the symbol ᮀ with either <, >, or ؍to make the resulting statement true. 4 ᮀ (f ) The negative of z is not greater than 3. (g) The quotient of p and q is at most 7. (h) The reciprocal of w is at least 9. (i) The absolute value of x is greater than 7. 8 (a) b is positive. (b) s is nonpositive. (c) w is greater than or equal to Ϫ4.

Hence, 4ac ϩ 2bc Ϫ 2ad Ϫ bd ϭ 2c͑2a ϩ b͒ Ϫ d͑2a ϩ b͒ ϭ ͑2c Ϫ d͒͑2a ϩ b͒. Note that if we factor 2ck Ϫ dk as k͑2c Ϫ d͒, then the last expression is ͑2a ϩ b͒͑2c Ϫ d͒. 3 39 Exercises 43 ͑2x ϩ y Ϫ 3z͒2 Exer. 1–44: Express as a polynomial. 44 ͑x Ϫ 2y ϩ 3z͒2 1 ͑3x ϩ 4x Ϫ 7x ϩ 1͒ ϩ ͑9x Ϫ 4x Ϫ 6x͒ 3 2 3 2 Exer. 45–102: Factor the polynomial. 2 ͑7x 3 ϩ 2x 2 Ϫ 11x͒ ϩ ͑Ϫ3x 3 Ϫ 2x 2 ϩ 5x Ϫ 3͒ 3 ͑4x 3 ϩ 5x Ϫ 3͒ Ϫ ͑3x 3 ϩ 2x 2 ϩ 5x Ϫ 7͒ 4 ͑6x Ϫ 2x ϩ x Ϫ 2͒ Ϫ ͑8x Ϫ x Ϫ 2͒ 3 2 46 4u2 Ϫ 2uv 47 3a2b2 Ϫ 6a2b 48 10xy ϩ 15xy2 49 3x 2y 3 Ϫ 9x 3y 2 50 16x 5y 2 ϩ 8x 3y 3 51 15x 3y 5 Ϫ 25x 4y 2 ϩ 10x 6y 4 52 121r 3s4 ϩ 77r 2s4 Ϫ 55r 4s3 53 8x 2 Ϫ 53x Ϫ 21 54 7x 2 ϩ 10x Ϫ 8 55 x 2 ϩ 3x ϩ 4 56 3x 2 Ϫ 4x ϩ 2 57 6x 2 ϩ 7x Ϫ 20 58 12x 2 Ϫ x Ϫ 6 59 12x 2 Ϫ 29x ϩ 15 60 21x 2 ϩ 41x ϩ 10 61 4x 2 Ϫ 20x ϩ 25 62 9x 2 ϩ 24x ϩ 16 63 25z2 ϩ 30z ϩ 9 64 16z2 Ϫ 56z ϩ 49 65 45x 2 ϩ 38xy ϩ 8y 2 66 50x 2 ϩ 45xy Ϫ 18y 2 67 36r 2 Ϫ 25t 2 68 81r 2 Ϫ 16t 2 69 z4 Ϫ 64w 2 70 9y4 Ϫ 121x 2 71 x 4 Ϫ 4x 2 72 x 3 Ϫ 25x 2 5 ͑2x ϩ 5͒͑3x Ϫ 7͒ 6 ͑3x Ϫ 4͒͑2x ϩ 9͒ 7 ͑5x ϩ 7y͒͑3x ϩ 2y͒ 8 ͑4x Ϫ 3y͒͑x Ϫ 5y͒ 9 ͑2u ϩ 3͒͑u Ϫ 4͒ ϩ 4u͑u Ϫ 2͒ 10 ͑3u Ϫ 1͒͑u ϩ 2͒ ϩ 7u͑u ϩ 1͒ 11 ͑3x ϩ 5͒͑2x 2 ϩ 9x Ϫ 5͒ 12 ͑7x Ϫ 4͒͑x 3 Ϫ x 2 ϩ 6͒ 13 ͑t ϩ 2t Ϫ 5͒͑3t Ϫ t ϩ 2͒ 2 2 14 ͑r 2 Ϫ 8r Ϫ 2͒͑Ϫr 2 ϩ 3r Ϫ 1͒ 15 ͑x ϩ 1͒͑2x Ϫ 2͒͑x ϩ 5͒ 16 ͑2x Ϫ 1͒͑x Ϫ 5͒͑x Ϫ 1͒ 8x y Ϫ 10x y 17 2x 2y 6a3b3 Ϫ 9a2b2 ϩ 3ab4 18 3ab2 2 2 3 19 45 rs ϩ 4st 3 3 3u3v4 Ϫ 2u5v2 ϩ ͑u2v2͒2 u3v2 2 20 3 6x2yz3 Ϫ xy2z xyz 21 ͑2x ϩ 3y͒͑2x Ϫ 3y͒ 22 ͑5x ϩ 4y͒͑5x Ϫ 4y͒ 73 x 2 ϩ 25 74 4x 2 ϩ 9 23 ͑x 2 ϩ 2y͒͑x 2 Ϫ 2y͒ 24 ͑3x ϩ y 3͒͑3x Ϫ y 3͒ 75 75x 2 Ϫ 48y 2 76 64x 2 Ϫ 36y 2 25 ͑x 2 ϩ 9͒͑x 2 Ϫ 4͒ 26 ͑x 2 ϩ 1͒͑x 2 Ϫ 16͒ 77 64x 3 ϩ 27 78 125x 3 Ϫ 8 27 ͑3x ϩ 2y͒2 28 ͑5x Ϫ 4y͒2 79 64x 3 Ϫ y6 80 216x9 ϩ 125y3 29 ͑x 2 Ϫ 3y 2͒2 30 ͑2x 2 ϩ 5y 2͒2 81 343x 3 ϩ y9 82 x 6 Ϫ 27y 3 31 ͑x ϩ 2͒2͑x Ϫ 2͒2 32 ͑x ϩ y͒2͑x Ϫ y͒2 83 125 Ϫ 27x 3 84 x 3 ϩ 64 85 2ax Ϫ 6bx ϩ ay Ϫ 3by 86 2ay2 Ϫ axy ϩ 6xy Ϫ 3x 2 87 3x 3 ϩ 3x 2 Ϫ 27x Ϫ 27 88 5x 3 ϩ 10x 2 Ϫ 20x Ϫ 40 35 ͑x1/3 Ϫ y1/3͒͑x 2/3 ϩ x1/3y1/3 ϩ y 2/3͒ 89 x 4 ϩ 2x 3 Ϫ x Ϫ 2 90 x 4 Ϫ 3x 3 ϩ 8x Ϫ 24 36 ͑x1/3 ϩ y1/3͒͑x 2/3 Ϫ x1/3y1/3 ϩ y 2/3͒ 91 a3 Ϫ a2b ϩ ab2 Ϫ b3 92 6w8 ϩ 17w4 ϩ 12 37 ͑x Ϫ 2y͒3 38 ͑x ϩ 3y͒3 93 a6 Ϫ b6 94 x 8 Ϫ 16 39 ͑2x ϩ 3y͒3 40 ͑3x Ϫ 4y͒3 95 x 2 ϩ 4x ϩ 4 Ϫ 9y2 96 x 2 Ϫ 4y 2 Ϫ 6x ϩ 9 41 ͑a ϩ b Ϫ c͒2 42 ͑x 2 ϩ x ϩ 1͒2 97 y 2 Ϫ x 2 ϩ 8y ϩ 16 98 y 2 ϩ 9 Ϫ 6y Ϫ 4x 2 33 34 ͑ 2x ϩ 2y ͒͑ 2x Ϫ 2y ͒ ͑ 2x ϩ 2y ͒2͑ 2x Ϫ 2y ͒2 40 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA 99 y 6 ϩ 7y 3 Ϫ 8 100 8c6 ϩ 19c3 Ϫ 27 101 x16 Ϫ 1 Exercise 104 x 102 4x 3 ϩ 4x 2 ϩ x I ?

48 ϫ 10Ϫ4 Many calculators use scientific form in their display panels. For the number c ϫ 10n, the 10 is suppressed and the exponent is often shown preceded by the letter E. For example, to find ͑4,500,000͒2 on a scientific calculator, we could enter the integer 4,500,000 and press the x 2 (or squaring) key, obtaining a display similar to one of those in Figure 6. 025 ϫ 1013. Thus, ͑4,500,000͒2 ϭ 20,250,000,000,000. Calculators may also use scientific form in the entry of numbers. The user’s manual for your calculator should give specific details.