Part 6

A REVIEW OF ALGEBRA

ORDER OF OPERATIONS, EVALUATION, PARENTHESES

Order of operations: First of all, raising to a power and extracting a root. Next, multiplication and division. Last of all, addition and subtraction.

Find the value of:

1. 5 . 2^2 - 25^(1/2) / 5 + 2^2 . 8 / 4 - 2.

2. (3 x 6 / 9)/2 - 2[100^(1/2)] / 5 + 4 . 2^3 - (14 . 2)/28.

3. 9 . 2 / 6 + 3 - 2 . 4^2 / 8^(1/3) - 4 + (3 . 2^2)/6.

Evaluate:

4. (a^4 - a^3 + b^3)/([a^2 b^2]^(1/2)) + (c[a^(1/2)] + a^3bc)/(abc), if a = 1, b = 2, c = 3.

5. t^(1/3) + ^(1/3) + m^(1/3), if t = 8, m = 27.

6. (2[3 + 2d + a]^(1/2))/(3[a + b - cx - c]^(1/2)) + ((3c - d)x)/(7ad - ^(1/2)), if a = 5, b = 3, c = -1, d = -2, x = 0.

7. a - {5b - [a - (3c - 3b) + 2c - 3(a - 2b - c)]}, if a = -3, b = 4, c = -5. (Yale.)

Simplify:

8. m - [2m - {3r - (4r - 2m)}].

9. 2a - [5d + {3c - (a + [2d - 3a + 4c])}].

10. 3c^2 + c(2a - [6c - {3a + c - 4a}]).

SPECIAL RULES OF MULTIPLICATION AND DIVISION

Give results by inspection:

1. (g + 1/2 k)^2.

2. (s - (2m)/3)^2.

3. (2v + 3w)(2v - 3w).

4. (x + 3ts)(x - 7ts).

5. (2l + 3g)(4l - 11g).

6. (a - (2b)/3 + c - d)^2.

7. (x^3 + 8m^3)/(x + 2m).

8. (y^3 - 27k^(3m))/(y - 3k^m).

9. (c^5 - d^5)/(c - d).

10. (e^5 + d^5)/(e + d).