MENTAL EXERCISE XXVIII. 6. Review.

Solve each of the following equations :

25. Show that -3-333 while - 2√2 ‡ 2√2.

26. Simplify()

exponents.

and express the result with positive.

27. Show that a, b, c, and d are proportional if

28. Express 2V in simplest form.

31. Find the geometric mean of a and 1/a.

32. Find the mean proportional between a and 1/a.

Classify each of the following progressions as being arithmetic

EXERCISE XXVIII. 7. Review

Simplify each of the following expressions :

1. 6 abc + (c + a)3 + (b + c)3 + (a + b) 3 − (a + b + c)3. 2. (x + y + z)2 + (x + y − z)2 — (y + z − x)2 — (≈ + x − y)2.

x

b-c

+

b2 — (c − a)2

a

b

C

3,

6. Show that (++)-(+) = 3

-a -b

if xa, xb, x + c.

7. Show that [(a− b)2 + (b − c)2 + (c − a)2]2

x-b

1

=

=(-1)"

+b\m-n b

14. For what value of n is a++ya homogeneous

binomial?

+4

15. For what value of n is "+13 + y2+ a homogeneous binomial?

16. Simplify

x2 + 2x√y + Y.
x + √ y

17. Square the complex number --√2.

18. Simplify (m + n + √ m − n) 6
n) 6 − (√m + n

19. Simplify

20. Rationalize the denominator of

√5+ √3 −√2

Solve each of the following equations:

21. √2+ √4x-3-√9x+1=0.

33. Expand (3x -1

= 9.

·xy - y =

x − xy + y2:

22,

=- - 2.

-2 by the binomial theorem. 34. Expand (1) by the binomial theorem.

35. Find the middle term in the expansion of

36. Find the middle term in the expansion of2 +

37. Find the middle term in the expansion of

14

38. In the expansion of (a+1)"

write the term which is free

from x.

39. Find the term free from x in the expansion of 40. Find the coefficient of a12b5 in (a + b)1.

INDEX.

NUMBERS REFER TO PAGES.