Exercises 6.3, page 194

1. $(x - 2) (x^{2} + 2 x + 4)$
3. $(x + 1) (x^{2} - x + 1)$
5. $(y - 5) (y^{2} + 5 y + 25)$
7. $(3 - t) (9 + 3 t + t^{2})$
9. $(2 a - 3 b) (4 a^{2} + 6 a b + 9 b^{2})$
11. $4 (x + 2) (x^{2} - 2 x + 4)$
13. $7 n^{2} (n - 1) (n^{2} + n + 1)$
15. $6 x^{3} y (9 - y^{3})$
17. $x^{3} y^{3} (x + y) (x^{2} - x y + y^{2})$
19. $3 a^{2} (a^{2} + 1) (a + 1) (a - 1)$
21. $\frac{4}{3} π (R - r) (R^{2} + R r + r^{2})$
23. $27 L^{3} (L + 2) (L^{2} - 2 L + 4)$
25. $(a + b + 4) (a^{2} + 2 a b + b^{2} - 4 a - 4 b + 16)$
27. $(2 - x) (2 + x) (16 + 4 x^{2} + x^{4})$
29. ${[(x - 1) (x^{2} + x + 1)]}^{2}$
31. $4 x (2 - x) (4 + 2 x + x^{2})$
33. $D (D - d) (D^{2} + D d + d^{2})$
35. $Q H (H + Q) (H^{2} - H Q + Q^{2})$
37. Expanding $(a + b) (a^{2} - a b + b^{2})$ verifies that it equals $a^{3} + b^{3} .$
39. $(x + y) (x - y) (x^{4} + x^{2} y^{2} + y^{4})$
41. $(n^{3} + 1) = (n + 1) (n^{2} - n + 1);$ If $n > 1,$ both factors are integers and greater than 1.

Get Basic Technical Mathematics, 11th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans