1. Operations with Monomials Operations with Polynomials

2. Monomial x A y3 2x 5xyz -3x2 4xy3 ¼ x3
A number, a variable or a product of a number and variable(s)
Examples: ½
x A y3
2x xyz
-3x xy3 ¼ x3
Not Monomials x x – 5
Isn’t this the same as

3. Quick Review
Exponent or power
base
Coefficient

4. Here is why this works…lets break the example down
The Laws of Exponents:
Multiplicative Law of Exponents: When multiplying monomials and
the bases are the same:
multiply the coefficients and add the exponents .
Here is why this works…lets break the example down

5. Example #1 Example #2 (3x2)(-6x3) (4y2z2)(y3) -18
1. Multiply the coefficients
1. Multiply the coefficients
2. Write down the bases in
alphabetical order
2. Write down the bases in
alphabetical order
3. Add the exponents of the
like bases
3. Add the exponents of the
like bases
4. Bring down any other exponents
4. Bring down any other exponents

6. Practice

7. The Laws of Exponents:
Exponential Law of Exponents: to raise a monomial to a power
- raise the coefficient to the power
- Multiply the exponents

8. The Laws of Exponents:
Exponential Law of Exponents: to raise a monomial to a power
- raise the coefficient to the power
- Multiply the exponents
to the 4th power = 16
Write the variables down
Multiply each variables exponent time the exponent on the outside of the parentheses

9. Practice

10. The Laws of Exponents: Division Law of Exponents:
When dividing monomials:
- simplify the coefficients
- subtract the exponents with same bases
- Simpify any Negative or Zero exponents

11. The Laws of Exponents: Division Law of Exponents:
When dividing monomials:
- simplify the coefficients
- subtract the exponents with same bases
- Simpify any Negative or Zero exponents

13. Practice

14. Binomial – 2 monomials connected by addition or subtraction
Trinomial – 3 monomials connected by addition or subtraction
Polynomial – 1 or more monomials connected by addition or subtraction
Like Terms – have the same variable and the same exponent

15. Add Polynomials – ignore the parentheses and combine like terms
1. Combine the term with the biggest exponent
2. Then combine the terms with next biggest exponent
3. Continue combing terms in descending order

16. Subtract Polynomials – distribute the negative 1 and combine like terms
1. Distribute the negative 1 (turn everything to its opposite)
2. Cross out the 2nd parentheses of original problem
3. Combine like terms, going in descending order

17. Add Polynomials – ignore the parentheses and combine like terms
1. Combine the term with the biggest exponent
2. Then combine the terms with next biggest exponent
3. Continue combining terms in descending order
Subtract Polynomials – distribute the negative 1 and combine like terms
1. Distribute the negative 1 (turn everything to its opposite)
2. Cross out the 2nd parentheses of original problem
3. Combine like terms, going in descending order