1. The document discusses multiplying and simplifying monomial expressions. It defines monomials and explains the rules for multiplying them, including adding exponents when multiplying like terms and multiplying all exponents when an expression is raised to a power. 2. The document also discusses multiplying monomials and polynomials using the distributive property and applying the same exponent rules. It provides examples of multiplying and simplifying expressions involving monomials and polynomials. 3. The learning objectives are to multiply monomials, simplify expressions with monomials, and to multiply a monomial and a polynomial.

1. Objectives
The student will be able to:
1. multiply monomials.
2. simplify expressions with monomials.
A-APR.1.1

2. A monomial is a
1. number,
2. variable, or
3. a product of one or more
numbers and variables.
Examples:
5
y
3x2y3

3. Why are the following not
monomials?
x + y
addition
x
y
division
2 - 3a
subtraction

4. REMEMBER YOUR EXPONENT PROPERTIES!!!!

5. Multiplying Monomials
When multiplying monomials, you
ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7

6. Simplify m3(m4)(m)
1. m7
2. m8
3. m12
4. m13

7. Power of a Power
When you have an exponent with an
exponent, you multiply those exponents.
1) (x2)3
x2• 3
x6
2) (y3)4
y12

8. Simplify (p2)4
1. p2
2. p4
3. p8
4. p16

9. Power of a Product
When you have a power outside of the
parentheses, everything in the
parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2

10. Simplify (4r)3
1. 12r3
2. 12r4
3. 64r3
4. 64r4

11. Power of a Monomial
This is a combination of all of the other
rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9

12. Simplify (3a2b3)4
1. 12a8b12
2. 81a6b7
3. 81a16b81
4. 81a8b12

13. Objectives
The student will be able to:
1. multiply a monomial and a
polynomial.
A-APR.1.1

14. Review: When multiplying variables,
add the exponents!
1) Simplify: 5(7n - 2)
Use the distributive property.
5 • 7n
35n - 10
- 5 • 2

15. 3
2) Simplify: a a 
(8 12)
4
a 8
a
3
 a
4
6a2 + 9a
3
4
12
3) Simplify: 6rs(r2s - 3)
6rs • r2s
6r3s2 - 18rs
- 6rs • 3

16. 4) Simplify: 4t2(3t2 + 2t - 5)
12t4
5) Simplify: - 4m3(-3m - 6n + 4p)
12m4
+ 8t3 - 20t2
+ 24m3n - 16m3p
YOUR TURN!!!

17. OH NO!! Fractions!! WHAT DO I DO!
…..the same as before…..
x
3
6) Simplify: (27x2 - 6x + 12)
-9x3 + 2x2 - 4x

18. Simplify 4y(3y2 – 1)
1. 7y2 – 1
2. 12y2 – 1
3. 12y3 – 1
4. 12y3 – 4y

19. Simplify -3x2y3(y2 – x2 + 2xy)
1. -3x2y5 + 3x4y3 – 6x3y4
2. -3x2y6 + 3x4y3 – 6x2y3
3. -3x2y5 + 3x4y3 – 6x2y3
4. 3x2y5 – 3x4y3 + 6x3y4