1. Drill #29 Simplify each expression.

2. Drill #30 Simplify each expression.

3. Drill #17 Simplify each expression.

4. Drill #20 Simplify each expression.

5. Drill #21 Simplify each expression.

6. Drill #22 Simplify each expression.

7. Drill #23 Simplify each expression.

8. Drill #24 Simplify each expression.

9. Drill #18 Simplify each expression. State the degree and coefficient of each simplified expression:

10. 6-1 Operations With Polynomials Objective: To multiply and divide monomials, to multiply polynomials, and to add and subtract polynomial expressions.

11. Negative Exponents * For any real number a and integer n, Examples:

12. Example: Negative Exponent *

13. Product of Powers * For any real number a and integers m and n, Examples:

14. Example: Product of Powers*

15. Quotient of Powers * For any real number a and integers m and n, Examples:

16. Example: Quotient of a Powers*

17. Power of a Power* If m and n are integers and a and b are real numbers: Example:

18. Example: Power of a Power*

19. Power of a Product* If m and n are integers and a and b are real numbers: Example:

20. Example: Power of a Product*

21. Example: Power of a Product

22. Power Examples* Ex1: Ex2: Ex3:

23. Find the value of r Find the value of r that makes each statement true:

24. Find the value of r * Find the value of r that makes each statement true:

25. Monomials Definition: An expression that is 1) a number, 2) a variable, or 3) the product of one or more numbers or variables. NOTE: variables must have WHOLE number exponents Constant: Monomial that contains no variables. Coefficients: The numerical factor of a monomial Degree: The degree of a monomial is the sum of the exponents of its variables.

26. State the degree and coefficient * Examples:

27. Polynomial* Definition: A monomial, or a sum (or difference) of monomials. Terms: The monomials that make up a polynomial Binomial: A polynomial with 2 unlike terms. Trinomial: A polynomial with 3 unlike terms Note: The degree of a polynomial is the degree of the monomial with the greatest degree.

28. Polynomials Determine whether each of the following is a trinomial or binomial…then state the degree:

29. Like Terms* Definition: Monomials that are the same (the same variables to the same power) and differ only in their coefficients. Examples:

30. To combine like terms To add like terms add the coefficients of both terms together Example

31. Adding Polynomials and Subtracting Polynomials

32. Multiplying a Polynomial by a Monomial To multiply a polynomial by a monomial: 1. Distribute the monomial to each term in the polynomial. 2. Simplify each term using the rules for monomial multiplication.

33. FOIL* Definition: The product of two binomials is the sum of the products of the F the first terms Othe outside terms Ithe inside terms Lthe last terms F O I L (a + b) (c + d) = ac + ad + bc + bd

34. The Distributive Method for Multiplying Polynomials* Definition: Two multiply two binomials, multiply the first polynomial by each term of the second. (a + b) (c + d) = c ( a + b ) + d ( a + b )

35. Examples: Binomials

36. The FOIL Method (for multiplying Polynomials)* Definition: Two multiply two polynomials, distribute each term in the 1 st polynomial to each term in the second. (a + b) (c + d + e) = (ac + ad + ae) + (bc + bd + be)

37. The Distributive Method for Multiplying Polynomials* Definition: Two multiply two polynomials, multiply the first polynomial by each term of the second. (a + b) (c + d + e) = c ( a + b ) + d ( a + b ) + e ( a + b )

38. Examples: Binomials x Trinomials

39. Classwork: Binomials x Trinomials

40. Pascals Triangle (for expanding polynomials) 1 121 1 3 31 14641 15 10 1051