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I. Model Problems.
II. Practice
III. Challenge Problems
VI. Answer Key
Web Resources
Monomials
www.mathwarehouse.com/algebra/polynomial/monomials/how-to-multiplymonomials.php
Polynomials
http://www.mathwarehouse.com/algebra/polynomial/
www.mathwarehouse.com/algebra/polynomial/how-to-multiply-polynomials.php
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I. Model Problems
A monomial is an expression that is a number, variable or product of a
number and variables. Examples of monomials: –3, 4x, 5xy, y2
To multiply monomials, multiply all the coefficients and all the
variables.
Example 1 Simplify 2x3(7x5).
= 14x3x5
Multiply the coefficients.
= 14x8
Multiply variables.
The answer is 14x8.
To divide monomials, divide the coefficients and the variables.
20x 7 y 6
Example 2 Simplify
.
4x 2 y 5
Divide the coefficients.
5x 7 y 6
= 3 5
x y
= 5x4y
Divide variables.
The answer is 5x4y.
When you have power of a power, everything inside the parentheses
gets raised to the power. You multiply exponents.
Example 3 Simplify (5x2y4)3.
= 53x2•3y4•3
Raise everything to the 3rd power.
= 125x6y12
Simplify.
The answer is 125x6y12.
To multiply rational expressions with monomials, in the numerator and
the denominator, follow the rules of simplifying monomials.
15x 7 y 6 xy 6
Example 4 Multiply
.

2x 2 y 5 5y 3
Multiply the numerators and the
15x 7 y 6  xy 6
= 2 5
denominators.
2x y 5y 3
15x 7 y 6  xy 6
=
10x 2 y 5  y 3
Multiply the coefficients.
15x 8 y12
=
10x 2 y 8
Multiply the variables (add
exponents).
3x 8 y12
=
2x 2 y 8
3
= x6 y4
2
Simplify coefficients.
Divide variables (subtract
exponents).
3 6 4
x y .
2
(3x 2 y 3 )3 4x 2 y 5

Example 5 Multiply
.
2x 2 y 5 18y 3
Simplify power to a power.
27x 6 y 9 4x 2 y 5

=
2x 2 y 5 18y 3
Multiply the coefficients and
108x 8 y14
=
variables.
36x 2 y 8
The answer is
3x 8 y14
= 2 8
x y
= 3x 6 y 6
The answer is 3x6y6.
Simplify coefficients.
Divide variables (subtract
exponents).
II. Practice
Simplify.
1. 4x5(9x3)
2. –9x5(7x7)
3. –7x5(3x2)
4. 20x4(3x9)
5. 8x7y5(10x2y)
6. –4x9 y15(3x9y5)
20x14
7.
10x 3
30x13
8.
15x 8
120x10
9.
10x 5
45y16
10.
9 y8
65x19 y17
11.
13x 5 y 5
30x 27 y 39
12.
5x10 y 8
13. (4x2y5)3
14. (2x3y2)5
15. (–2x3y7)3
16. (7x2yz4)2
17. (10x24y20)2
18. (–3x5y10)3
3x 6 y11 20x 5 y 8

19.
10x 2 y 5 12x 4 y 3
24x12 y 23 15x 3 y 3

20.
4x 7 y 20 25x 2 y 2
24x19 y 20 15x12 y19

21.
12x17 y14 3x 9 y15
14x 8 y 6 (2x 3 y 3 )2

22.
7x 3 y 3
2x 2 y
III. Challenge Problems
23. What is the area of a rectangle with length 6xy7 inches and width
(5x2y) inches? Write your answer as an expression in terms of x and y.
20x19 y 20 4x54 y19 z 20 (4x12 y19 z)3
24. Simplify
.


8x17 y14 (2x 9 y15 )3 3x 4 y15 z 2
25. Correct the Error
There is an error in the student work shown below:
Question: (3x4y9)5 .
Solution:
= (3x4y9)5
= 15x20y45
What is the error? Explain how to solve the problem.
_________________________________________________________
_________________________________________________________
IV. Answer Key
1. 36x8
2. -63x12
3. -21x7
4. 60x13
5. 80x9y6
6. -12x18y20
7. 2x11
8. 2x5
9. 12x5
10. 5y8
11. 5x14y12
12. -6x17y31
13. 64x6y15
14. 32x15y10
15. -8x9y21
16. 49x4y2z8
17. 100x48y40
18. -27x15y30
19. (1/2)x6y11
20. (18/5)x6y4
21. 10x5y10
22. 4x9y8
23. 30x2y8 in2
24. (80/3)x61y22z21
25. The student multiplied the coefficient by the exponent instead of
raising the coefficient to the power. The correct answer is 243x20y45.