350 ALGEBRA.
EXAMPLES XXXVII. b.
In the following expansions find which is the greatest term:
1. (x+y)17 when x = 4, y = 3. 2. (x - y)28 when x = 9, y = 4. 3. (1 + x)4 when x = 2 3 . 4. (a-4b)15 when a = 12, b = 2. 5. (7x-2y)^30 when x=8, y = 14. 6. (2x+3)^n when x = 5 2, n = 15. 7. In the expansion of (1 +x)25 the coefficients of the (2r + l)th and (r + 5)th terms are equal : find r, 8. Find n when the coefficients of the 16th and 26th terms of (1 + x)n are equal. 9. Find the relation between r and n in order that the coefficients of (r + 3)th and (2 r — 3)th terms of (1 + x)3n may be equal. 10. Find the coefficient of x^n in the expansion of (x2+1 x)2m 11. Find the middle term of (1+x)2n in its simplest form. 12. Find the sum of the coefficients of (x + y)^16. 13. Find the sum of the coefficients of (3x+y)^9. 14. Find the rth term from the beginning and the rth term from the end of (a + 2x)^n. 15. Expand (a^2 + 2a + 1)^3 and (x2 - 4 x + 2)^3.
Expand to four terms the following expressions :
16. (1+x)1 3. 17. (1+x)3 4. 18. (1+x)2 3. 19. (1+3x)-2. 20. (1-x2)-3. 21. (1+3x)-4. 22. (2+x)-3. 23. (1+2x)-1 2. 24. (a-2x)-3 2.
Write in simplest form :
25. The 5th term and the 10th term of (1 + x)-3 2. 26. The 3d term and the 11th term of (1 + 2x)11 2. 27. The 4th term and the (r + 1)th term of (1 + x)^-2. 28. The 7th term and the (r + 1)th term of (1 - x)^-1 2. 29. The (r + 1)th term of (a-bx)-1, and of (1 - nx)1 n.
Find to four places of decimals the value of
30. 3 122. 31. 4 620. 32. 5 31. 33. 1 99.
