### INTRODUCTORY EXERCISES - Symbol Manipulation

(1) Simplify. Expand any products.

``` (a) 4y - (6 - 3x + y)

(b) (2 + 13/3)(9/52)

(c) (4/x)-1

(d) 3 - (1/2)(-x2 + x + 2) - 5(1.2x2 - 2.7)

(e) 2r2 + 4(2r)(100/r2)

(f) -36(x - 1)(x + 2)

```
SOLUTION:
``` (a)  4y - (6 - 3x + y)
4y - 6 + 3x - y
3y - 6 + 3x
3y + 3x - 6

(b) (2 + 13/3)(9/52)
( 2(3)/3 + 13/3 )(9/52)  --common denominator of 3
(6/3 + 13/3)(9/52)
(19/3)(9/52)
(19)(3)/(52)   --in the step above, a common factor of 3 can be cancelled
from the numerator and denominator

(c) (4/x)-1

1         1         x
-----  =  -----   =  ---
(4/x)1    (4/x)       4

(d)  3 - (1/2)(-x2 + x + 2) - 5(1.2x2 - 2.7)
3 + (x2/2) - (x/2) - (2/2) - 5(12/10)x2 + 5(27/10)
3 + (x2/2) - (x/2) - 1 -(60/10)x2 + (27/2)

x2 - 60x2  -  x   + 3 - 1 + 27
---   ----    ---           ---
2     10      2             2

x2 - 12x2  -  x  +  6  -  2  + 27    ---find common denominators
---  ----   ---   ---   ---  ---
2    2      2     2     2    2

-55x2 -  x  +  31
-----   ---   ---
10      2     2

-11x2 -  x  +  31
-----   ---   ---
2      2     2

(e) 2r2 + 4(2r)(100/r2)
2r2 + 4(2)(100/r)    ---cancel common factor of  2r from both
numerator and denominator
2r2 + (800/r)

2r3 + 800         ---find common denominator
----   ---
r      r

2r3 + 800
----------
r

(f) (2x - 1)2 = (2x - 1) (2x - 1) = 22x2 - 2x  - 2x + 1
= 4x2 - 4x +1

```