Chapter 1: Expanding Expressions
Section 1.1 Order of Operations
1. $-4$ 3. 7 5. 4 7. 2 9. ${\scriptstyle{}^{2}\!\!\diagup\!\!{}_{3}\;}$ 11. 2
13. 16 15. 30 17. 1 19. $-{\scriptstyle{}^{25}\!\!\diagup\!\!{}_{4}\;}$
Section 1.2 Substitution
1. 16 3. 51 5. 5 7. $-10$ 9. 22 11. 30
13. 30 15. $-71$ 17. $-6$ 19. $-25$ 21. 8 23. ${\scriptstyle{}^{25}\!\!\diagup\!\!{}_{2}\;}$
25. ${\scriptstyle{}^{3}\!\!\diagup\!\!{}_{8}\;}$ 27. 8 29. $-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$
Section 1.3 Linear Equations 1
1. 2 3. 3 5. ${\scriptstyle{}^{17}\!\!\diagup\!\!{}_{2}\;}$ 7. ${\scriptstyle{}^{41}\!\!\diagup\!\!{}_{7}\;}$ 9. ${\scriptstyle{}^{7}\!\!\diagup\!\!{}_{6}\;}$ 11. $-{\scriptstyle{}^{23}\!\!\diagup\!\!{}_{2}\;}$
13. ${\scriptstyle{}^{51}\!\!\diagup\!\!{}_{11}\;}$ 15. $-{\scriptstyle{}^{15}\!\!\diagup\!\!{}_{14}\;}$ 17. $-{\scriptstyle{}^{11}\!\!\diagup\!\!{}_{8}\;}$ 19. ${\scriptstyle{}^{a}\!\!\diagup\!\!{}_{2}\;}$ 21. $\tfrac{10-2a}{11}$ 23. $7-3a$
25. $\tfrac{5a-3p}{12}$ 27. $\tfrac{{{b}^{2}}}{4a}$ 29. $\tfrac{3ab}{2a-3b}$ 31. 6 33. 6 35. 5
37. 2 39. 6 41. $-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$
Section 1.4 Word Problems
1. 15, 15, and 8 inches 3. 22 inches × 75 inches 5. 11 feet × 31 feet
7. 13 feet × 20 feet 9. 12, 15, 12, 12, 15 in. 11. 29
13. 60 15. 120 17. 6 hrs. 19. 10 21. 5 23. Becky is 34.
25. Lukas is 34; 27. 78 dimes; 29. 167 nickels;
Marten is 37; 85 quarters. 220 dimes.
Stefan is 39. 31. 21 nickels; 16 quarters.
Section 1.5 Multiplying Polynomials
1. ${{x}^{2}}+9x+14$ 3. ${{x}^{2}}+11x+24$ 5. ${{x}^{2}}-8x+15$ 7. ${{x}^{2}}-5x-14$
9. ${{x}^{2}}+5x-24$ 11. ${{x}^{2}}-9x+20$ 13. ${{x}^{2}}-10x+21$ 15. ${{x}^{2}}+11x-12$
17. ${{x}^{2}}-3x-18$ 19. ${{x}^{2}}-4x-21$ 21. ${{x}^{2}}+20x+36$ 23. ${{x}^{2}}-9x-36$
25. ${{x}^{2}}-x-56$ 27. ${{x}^{2}}-4x-12$ 29. ${{x}^{2}}+x-6$ 31. ${{x}^{2}}-1$
33. ${{x}^{2}}-36$ 35. ${{x}^{2}}+3x-28$ 37. ${{x}^{2}}-25$ 39. ${{x}^{2}}-81$
41. $2{{x}^{2}}-x-10$ 43. $9{{x}^{2}}-25$ 45. $25{{x}^{2}}-49$ 47. ${{x}^{4}}-1$
49. $9{{x}^{2}}-1$ 51. $100-9{{x}^{2}}$ 53. $4{{t}^{2}}-25{{K}^{2}}$ 55. ${{x}^{2}}-6x+9$
57. ${{x}^{2}}+2x+1$ 59. $4{{x}^{2}}-12x+9$ 61. ${{x}^{2}}+8x+16$ 63. ${{x}^{2}}+16x+64$
65. $25{{x}^{2}}+30x+9$ 67. $2{{x}^{2}}-5x-12$ 69. ${{x}^{2}}+2ax+{{a}^{2}}$ 71. ${{K}^{2}}{{x}^{2}}+2Kxt+{{t}^{2}}$
73. $12{{x}^{2}}-5x-2$ 75. ${{x}^{4}}-6{{x}^{2}}+9$ 77. ${{x}^{4}}-4{{x}^{2}}+4$ 79. $9{{x}^{4}}+6{{x}^{2}}+1$
81. ${{x}^{4}}+2{{x}^{2}}y+{{y}^{2}}$ 83. $25{{x}^{2}}-20{{x}^{3}}+4{{x}^{4}}$ 85. $6{{x}^{3}}-5{{x}^{2}}-3x+2$
87. $9{{x}^{2}}-6x+1+15Kx-5K$ 89. $4{{t}^{2}}-9{{K}^{2}}$ 91. ${{x}^{3}}-4{{x}^{2}}-19x+6$
93. ${{x}^{2}}-{{t}^{2}}+4t-4$ 95. $2{{x}^{2}}+ax-15{{a}^{2}}$ 97. $6{{x}^{2}}+5ax-21{{a}^{2}}$
99. $6{{x}^{3}}-7{{x}^{2}}+4x-1$
Section 1.6 Combining Like Terms
1. $5{{x}^{2}}y+2x{{y}^{2}}$ 3. $-8{{x}^{2}}yz-2xyz$ 5. $5+3x+3y$ 7. $2{{x}^{2}}+3x-17$
9. $10x+10$ 11. $12x$ 13. $27$ 15. $6x+13$
17. $-4a+{{x}^{2}}a$ 19. $3{{x}^{2}}+19x-59$
21. a. $-5$ b. $-12x$ c. \[4{{x}^{2}}\] d. \[-13\] 23. a. False b. False c. True
d. True e. True 25. a. $-5x+2$ b. $10{{x}^{2}}-x$ c. \[9{{x}^{3}}-6{{x}^{2}}\]
Section 1.7 Parentheses and Minus Signs
1. $-4{{x}^{2}}+2x+3$ 3. $16x$ 5. $10{{x}^{2}}-15$ 7. ${{x}^{2}}-{{a}^{2}}$ 9. $20t-11$
11. $-6{{x}^{2}}+4x-5$ 13. $16{{x}^{2}}-12$ 15. $6{{x}^{2}}-4x-1$ 17. $-5x+23$ 19. $-2x+6$
21. 1 23. $\tfrac{-x+18}{3}$ 25. $-\tfrac{6}{5}$ 27. $\tfrac{11y-23}{12}$ 29. $-\tfrac{5}{4}$