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Exercises 1.8, page 35

1. $- 8 s^{8} t^{13}$
3. $x^{2} - 5 x + 6$
5. $a^{3} x$
7. $- a^{4} c^{3} x^{3}$
9. $- 8 a^{3} x^{5}$
11. $i^{3} R + 2 i^{3}$
13. $- 3 s^{3} + 15 s t$
15. $5 m^{3} n + 15 m^{2} n$
17. $- 3 M^{2} - 3 M N + 6 M$
19. $x^{4} t y + x^{3} t y^{4}$
21. $x^{2} + 2 x - 15$
23. $2 x^{2} + 9 x - 5$
25. $y^{2} - 64$
27. $6 a^{2} - 7 a b + 2 b^{2}$
29. $6 s^{2} + 11 s t - 35 t^{2}$
31. $2 x^{3} + 5 x^{2} - 2 x - 5$
33. $x^{2} - 4 x y + 4 y^{2} - 16$
35. $2 a^{2} - 16 a - 18$
37. $18 T^{2} - 15 T - 18$
39. $- 2 L^{3} + 6 L^{2} + 8 L$
41. $9 x^{2} - 42 x + 49$
43. $x_{1}^{2} + 6 x_{1} x_{2} + 9 x_{2}^{2}$
45. $x^{2} y^{2} z^{2} - 4 x y z + 4$
47. $2 x^{2} + 32 x + 128$
49. $- x^{3} + 2 x^{2} + 5 x - 6$
51. $6 T^{3} + 9 T^{2} - 6 T$
53.
1. $49 \neq 9 + 16$
2. $1 \neq 9 - 16$
55. ${(x + y)}^{3} = x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$
57. $P + 0.02 P r + 0.0001 P r^{2}$
59. $2 w^{2} + 30 w + 100$
61. $3 R^{2} - 4 R X$
63. $n^{2} + 200 n + 10, 000$
65. $R_{1}^{2} - R_{2}^{2}$

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