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Exercises for Section 1.3 Simplify the following expressions. 1. 5x5 + 4x4 + x3 + x5 + 5x4 + 3x3 2. 2xy + 14xy + 3xy2 + 7xy 3. ex + ex + ex + 7 4. 7 + lnx + lnx + 5lnx 5. (a - b) + (a - b) + (a + b) Add the following polynomials. 6. (2x + 3y + 2) + (7x + 7y + 7) 7. (3m2 + 2mn + 3n2 ) + (11m2 + 7n2 + 5mn) 8. (a + b) + (2a + 3a) + (4b + 2a) + b 9. (2e + 7) + (15e - 3) 10. (ax + bx + x) + (bx + x + 2ax) Simplify the following expressions. 11. x -x x x x 1 2e + e - 7e + 8e - e 12. 12 3 1 2 xy - xy + xy - xy 2 7 8 21 13. (2x - 1) + (2x + 1) - (2x - 1) 14. (2x + 1)3 + (2x - 1)2 - (2x + 1)2 15. Ax2 + 2x + Bx2 - x + A - B Simplify the following. 16. (x - y) + (y - z) + (z - w) + (w - v) 17. 13x - 7x - 6x - 6 18. ex - ex + ex - 7 19. (7 - tx) - (tx + 5tx) 20. (a - b) - (a - b) -2(a - b) Simplify the following 21. (2xy - 7x2 + 2xy2 - 11y2) - (9x2 - 3xy2 + 14y2) 22. 2c2 + 3d3 - e - (-7c2 - e + 6d3) 23. (a + b) + (a + b) + (a + b) - (a + b) 24. (2xnym - 3xn-1ym + 2xn-1ym) - (2xnym - 2xn-1ym) 25. 22ab2 - 84a2b - ( 3 4 ab2 - 8a2b + 33 1 3 a2b) 26. 16x2y - 32x2y - 82xy2 + 63x2y 27. (1 - log(x)) - (1 + log(x)) - 30 - 28. Bc2 + 5d2 - u - (-7c2 - u + 1 2 d2) 29. (2a + 1) + (6a + 1) + (6a - 1) - (a - 2) 30. (x - y) + (w + v) + (x + v) + (w - x) + (-v - x) - (x - y). Simplify. 31. (7c + 2cd - 7d2) + (2c - 7cd + 2d2) + (6c - 6cd + 6d2) 32. (16x2 + 3xy - 7x) + (42x2 - 7xy + 10x) + (-18x2 + x - 41) 33. (6x2 - 3x1 + 2x0) + (-13x2 + 14x1 -37x0+ 1 2 ) + (32x2 + 32x1 -30x0 - 7 2 ) 34. (4a2b + 62ab - 16b2) - (60ab - 4a2b - 7b2) 35. ((a + b)2 + 4) + (-17(a + b)2 - 8) + (11(a + b)2 - 7) + ( 1 2 (a + b)2 + 1 2 ) 36. ( 1 2 y - 3xy) + (4xy - 3 4 y) + (5xy) 37. (14a + 19b + 4c - 2) + (12a - 21b - 12c + 7) + (-4a + 6b - 10c - 10) 38. (6xn + 2xnyn - 3yn) - (-17xn + 14xnyn - 4yn) 39. (8c3 - 22cp2 + 45p3) + (9c3 - 21c2p - 42p3 ) + (-6p3 - 19c2p - 20p3) 40. (1.7x - 3.2y + 7.5z + 8) + (-.1x - 3.7y + 1.1z - 18) + (-x + y + .8z + .8) Simplify 41. 4x2 - 3x3 + 2x - x3 + 7 - 11x - 7x3 - 3 + x 42. 4c - 5d + 7e - 21d - 14e + 5c - 7c + 4d 43. ex - 7e2x - e + 7ex + 5e + 3ex - 9e2x + 17e - 3ex 44. yx - 7 + 2yx - x - 3yx + 2 45. -7xy2 + 2y - 3xy + 7y - 49xy2 - 7xy + 16y 46. 22v - 3w + 7u - (19v + w - 7v + 2u - 18w) 47. (a2 + b) - (a2 + b) + (a2 - b) - (-a2 - b) 48. (p - w) + (r + s) + (p + s) + (r - p) + (- s - p) + (-p - w) 49. (x + a - y + b) - (2x + a - 2y + c) + (2a - 3y + c) 50. (mx + b) + (-3mx - 2b) - (6mx + 6b) 51. (3a2 - a - 5) + (2a + 2a2 + 5) + (2a2 - a) 52. (16a7 + 32a6 + a5 - 16a6) - (51a7 - 15a5 + 91a7) 53. (5a4 - 5a3 + 5a2 - 5a) - (-11a4 + 11a3 - 11a2 + 5a) 54. (vx + w) + (-3vx - 2w) + (-6vx + 6w) 55. xy2 + x3y2 - 15x3y2 - 19x2y + 22xy2 - 24xy2 + 45x3y2 56. 9(a +h) -9a h

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