By Sheldon Axler

University Algebra and Trigonometry will entice those that are looking to provide vital themes extra in-depth, higher-level insurance. this article deals streamlined process observed with available definitions throughout all chapters to permit for an easy-to-understand learn. collage Algebra comprises prose that's distinctive, exact, and straightforward to learn, with simple definitions of even the themes which are mostly such a lot tough for readers.

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A z(z − a) 2 − + 2 y −4 + x+3 5 45. 38. x−3 5 − 4 y +2 46. 39. 16. (b − 3)(b + 3)(b2 + 9) 17. xy(x + y) 37. 1 y 40. 1 a 19. (t − 2)(t + 2t + 4) 4t + 1 3 + t2 t 3 v+1 + v(v − 2) v3 21. (n + 3)(n2 − 3n + 9) 42. w−1 2 − w3 w(w − 3) For Exercises 23–50, simplify the given expression as much as possible. 43. 1 x y − x−y y x 23. 4(2m + 3n) + 7m 44. 1 1 1 − y x−y x+y 3 2 20. (m − 2)(m + 2m + 4m + 8m + 16) 22. (y + 2)(y 4 − 2y 3 + 4y 2 − 8y + 16) 24. 3 2m + 4(n + 5p) + 6n − a 47. x−2 y z x+2 48. x−4 y+3 y−3 x+4 49.

5 · 3 · 2 + 6 · 4 For Exercises 5–22, expand the given expression. 6. (x + y − r )(z + w − t) 2 8. (3b + 5) 9. (2c − 7)2 2 10. (4a − 5) 11. (x + y + z)2 2 12. (x − 5y − 3z) 13. (x + 1)(x − 2)(x + 3) 14. (y − 2)(y − 3)(y + 5) 15. (a + 2)(a − 2)(a2 + 4) 1 x 1 z 2 18. a z(z − a) 2 − + 2 y −4 + x+3 5 45. 38. x−3 5 − 4 y +2 46. 39. 16. (b − 3)(b + 3)(b2 + 9) 17. xy(x + y) 37. 1 y 40. 1 a 19. (t − 2)(t + 2t + 4) 4t + 1 3 + t2 t 3 v+1 + v(v − 2) v3 21. (n + 3)(n2 − 3n + 9) 42. w−1 2 − w3 w(w − 3) For Exercises 23–50, simplify the given expression as much as possible.

3 5 2 2 115 76 1 2 1 3 3 0 1 2 3 3 1 12 7 2 257 101 3 Some rational numbers on the real line. We will use the intuitive notion that the line has no gaps and that every conceivable distance can be represented by a point on the line. With these concepts in mind, we call the line shown above the real line. We think of each point on the real line as corresponding to a real number. The undefined intuitive notions (such as “no gaps”) can be made precise using more advanced mathematics. In this book, we let our intuitive notions of the real line serve to define the system of real numbers.