Download 1. Simplify the following expressions

Practice for 6.1 – 6.3
1. Simplify the following expressions:
2 x 2  11xy  21y 2 10 x 2  xy  2 y 2
a)

4 x 2  8 xy  3 y 2 5 x 2  37 xy  14 y 2
x3  8y3
3x 2  5 xy  8 y 2

c)
3x 2  2 xy  16 y 2 x 2  2 xy  4 y 2
e)
3x  2
x2  x  2
x2  x  6


3x 2  x  2 5 x 2  14 x  3 5 x 2  26 x  5
Math 71
Name:
b)
3a 2  13ab  10b 2 3a 2  7ab  6b 2

7a 2  34ab  5b 2 2a 2  5ab  3b 2
d)
25 x 2  50 xy  y 2 10 x 2  13xy  3 y 2

125 x 3  y 3
25 x 2  5 xy  y 2
f)
7x  4
4x  5
 2
6x  7 x  3 6x  7 x  3
2
g)
3x  2
7x  5
 2
2 x  9 x  5 4 x  8x  5
2
3
2
x y 2 xy 3
1
5
 2
3 xy xy
2
i)
x
x2
4
 2

x  3 x  2x  3 x  1
j)
x 1  y 1
x 1  3 y 1

3
1
 2
a  10a  25 a  a  2
4
2
 2
2
a  6a  5 a  3a  10
2
k)
h)
Practice for 6.4 – 6.7
1.
Perform the following division:
5 x 2 yz 2  15 x 3 y 2 z  30 x 2 y 3 z 3
a)
5x 2 y 2 z
b)
2.
Perform the following division by synthetic division:
7 x 4  5 x 3  2 x 2  3x  8
x3
3.
Solve the following equations for x:
3x  5
7
6


a)
2
6 x  7 x  3 2 x  3 3x  1
b)
5x 3  2 x 2  1
x3
4
1
2
 2
 2
x  3x  10 x  9 x  20 x  2 x  8
2
4. Solve the equation
1 1 1
for q.
 
3 p q 2r
5. The rate of the jet stream is 100 mph. Traveling with the jet stream, an airplane can fly 2400 miles in the amount
of time as it takes to fly 1600 miles against the jet stream. What is the airplane’s average rate in calm air?
6. It takes John to finish painting his room in 5 hours while it takes Thomas to paint the same room in 3 hours.
Working together, how long will it take both to paint John’s room?