1. Drill #17 Simplify each expression.

2. Drill #18 Simplify each expression.

3. Drill #19 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: Power of a Power*

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. Power Examples* Ex1: Ex2: Ex3:

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

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

24. Monomials* Definition: An expression that is 1) a number, 2) a variable, or 3) the product of one or more numbers or variables. 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.

25. State the degree and coefficient * Examples:

26. 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.

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

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

29. Adding Polynomials* To add like terms add the coefficients of both terms together Examples

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

31. Subtracting Polynomials* To subtract polynomials, first distribute the negative sign to each term in the polynomial you are subtracting. Then follow the rules for adding polynomials. EXAMPLE:

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