1. Messin with Monomials
Hey whatz
a monomial???

2. Monomials defined
A number like 6, 10, or 958(called a constant or a constant monomial)
A variable like x, y, or z
A product ( that means multiply) of a number and one or more variables

3. Polynomials Definition: the sum of monomials Special names:
Binomial: is the sum of two terms
xy + 3x
Trinomial: is the sum of three terms
a + ab + 6

4. Some examples of Monomials
Like Terms
7xyz, 9xyz, and ½xyz
6x, 5x, and 102x
Unlike Terms
9x and 4 y
3ab, 3 bc, and 8 abc

5. Adding Monomials is Magic!!!
When monomials have exactly the same variables including the same exponents they are called LIKE TERMS
LIKE TERMS can be added by adding their coefficients

6. Monomials Added
Notice that the coefficients are added but the variable and the exponent remain the same.

7. More Monomials Added
Be sure to compare variables and exponents before adding coefficients
They must be exactly the same
If they are not LEAVE THEM ALONE

8. Degree
Of a variable
This just means the number of times the variable occurs as a factor in the monomial
The x is of degree 2
Of a monomial
This means the sum of the degrees of the variables
The degree of
is = 7

9. Note
The degree of any non zero constant monomial such as 12 is 0

10. The Degree of a Polynomial
Is the greatest of the degrees of its terms after it has been simplified.

11. Monomials Multiplied
To multiply these monomials
Rearrange

12. Rule for Multiplying Monomials
It’s easy. Just remember to
ADD the
Exponents

13. Monomial Raised to a Power
This means to repeatedly multiply the monomial So
Means

14. Rule for Raising Monomials to a Power
It’s easy. Just remember to
Multiply the
Exponents