Expert: Richard J. Raridon - 11/1/2010

Question

1. Simplify:  

z3 - 4z
z2 - 4z + 4
z  z
4

z (z + 2)
z - 2
 z2 + 2z
2  


2. Simplify:  

(a - x)2
x2 - a2
1  x - a
x + a

x - a  -a - x
x + a


3. Simplify:  

9 - 4z2
6z2 - 5z - 6
-1  -3 - 2z
3z + 2

3 + 2z
3z - 2
 3 + 2z
3z + 2


4. Simplify:  

(t + 1) (t2 - 1)
(t - 1) (t + 1)2
1  t - 1
t + 1

-1  t + 1
t - 1


5. Simplify:  

t4 - c4    
(t + c)2 (t2 + c2)
t + c
t - c
 1
-1  t - c
t + c


6. Find the domain of the function:  

h(y) = (y3-8)(y+2)-3

D = {y ≠ -2}  D = {y ≠ -3}
D = {y ≠ 1}  D = {y ≠ 2}

7. Find the domain of the function:   

(t + 1) (t + 4)
t - 1    
D = {t ≠ 1}  D = {t ≠ -1}
D = {  }  D = {t ≠ -4}

8. Simplify:  

x4 - 2x2y2 + y4   
x4 - x3y - xy3 + y4
1  (x + y)2   
x2 + xy + y2

-1  (x - y)2   
x2 + xy + y2


9. Solve:

3p-7 = 8

p = 5  p = -5
p = 0.33  p = 3

10. Simplify:

z(z-1) = z(z+1)

z = 2  z = 0
z = 0.5  z = -2

11. Simplify:  

2a2 = 7a+4

a = 0.5 or -4  a = -0.5 or 4
a = 0.5 or 4  a = 2 or -4

12. Simplify:  

(n-1)2 = 1

n = -2 or 0  n = 0 or -1
n = 2 or 1  n = 0 or 2

13. Simplify:

m2 = m

m = 0 or -1  m = -1 or -2
m = 1 or -1  m = 0 or 1

14. Solve:  

4(3d-5) = 2(5d+1)

d = 11  d = 20
d = 10  d = 22

15. Simplify:  

-26 ÷ 39
25 20
-15
8
 -507
250

-8
15
 8
15


16. Simplify:  

22z2    -5  
15  11z3
-2
5z
 -2
3z

-242z5
15
 -5
3z


17. Simplify:  

28x ÷ 21x3
25 15
4
5x2
 5x2
4

196x2
125
 14x
5


18. Simplify:   

2uv ÷ 2u2 ÷ 2v2
v u
2  u
2v

-2  1
2


19. Simplify:  

7x2 ÷ [4x] ∙  35  -1
9y [15y2] 6xy
2x2y2  x2y2
2

2
x2y2
 3x2y2
2


20. Simplify:  

t - 2    t2 + 2t - 3  
t + 3  t2 - t - 2
1  t + 1
t - 1

-1  t - 1
t + 1


21. Simplify:  

 x2     x + 1  ÷    x     
x + 1  x + 2 (x + 1) (x + 2)
x + 1
x + 2
 -x(x-1)
x2 - x - 2
x + 2   
 x(x+1)

22. Simplify:  

3x2 - 8x + 4 ÷ 3x2 - 5x - 2
9x2 - 4   9x2 - 3x - 2
3x2 + 2
3x2 - 2
 3x - 2
3x + 2

3x + 2
3x - 2
 -3x + 2
3x2  


23. Simplify:  

 x2 - y2   
x + y
 x4 - y4   
x2+y2  1
1
(x2+y2)(x+y)
 x4-y4

24. Simplify:  

7 + 11 - 9
10 20 20
9
10
 4
5

9
5
 4

25. Simplify:  

2 - 3 + 4
3 5 15
1
6
 1
3

-1
5
 -1
3


26. Simplify:  

7 - 1 + 19
12 20
-3
8
 25
32

8
15
 7
16


27. Simplify:  

x + 3 - 2x + 1
5   10  
0.5  2x - 1
5  

-2  4x - 5
10  


28. Simplify:  

x + 3 + x - 2
5   2x  
1
2
 2x2
-2x  2x2 + 11x - 10
 10x   


29. Simplify:  

2 - 5
3 6
1 + 2
3 9
-3
10
 -10
3

1
4
 -1
4


30. Simplify:  

z - 1
z
1 - 1
z
1  z-1
z - 1  z+1

31. Simplify:  

a-2 - b-2
a-1 + b-1
b - a
ab  
 1
ab

b + a
ab  
  ab  
b - a


32. Simplify:

1 - 1
p2 q2
2 - 1 - 1
p2 pq q2
1
2
 q + p
2q + p

1  1
q


33. Simplify:  

x-2 - x2
x-1 - x
x2  1 + x
1 + x2
x  
 x² + 1

34. Simplify:

1 - 1
x y
y - x
x y
1   1  
y - x

y + x   1  
y + x

Answer
1. z^3-4z = z(z+2)(z-2)   z^2-4z+4 = (z-2)^2
2. (a-x)^2 = a^2-2ax+x^2   x^2-a^2 = (x-a)(x+a)
3. 9-4z^2 = (3-2z)(3+2z)   6z^2-5z-6 = (3z+2)(2z-3)
4. (t+1)(t^2-1) = t^3+t^2-t-1  (t-1)(t+1)^2 = t^3+t^2-t-1
5. (t^4-c^4) = (t^2+c^2)(t-c)(t+c)  
(t+c)^2(t^2+c^2) = t^4+2t^3c+2t^2c^2+2tc^3+c^4
6&7 I don't do domains
8. x^4-2x^y^2+y^4 = (x^2-y^2)^2
9. p=5
10. z=0
11. a = 4, -0.5
12. n = 0, 2
13. m = 0, 1
14. d = 11
15. -2/3
17. 4/(3x^2)
18. 2v^3/u
20. t^2-2t-3 = (t-3)(t+1)
22. (3x-2)/(3x+1)
x^2-y^2 = (x+y)(x-y)   x^2-y^4 = (x^2+y^2)(x-y)(x+y)