1. Prepared by: David Crockett Math Department Lesson 73 -- Factoring the Difference of Two Squares -- Probability Without Replacement

2. Prepared by: David Crockett Math Department Background: Remember when multiplying two binomials we use the FOIL method. Factoring the Difference of Two Squares Observe the following special case: When we multiply two binomials that are the sum and difference of the same two numbers we have: = a 2 ab b 2 = a 2 b 2 In this lesson we are factoring (the inverse of multiplying) so… we reverse everything in the above example: Factor: a 2 b 2

3. Prepared by: David Crockett Math Department Example 73.1 Factoring the Difference of Two Squares Factor:

4. Prepared by: David Crockett Math Department Example 73.2 Factoring the Difference of Two Squares Factor:

5. Prepared by: David Crockett Math Department Example 73.3 Factoring the Difference of Two Squares Factor:

6. Prepared by: David Crockett Math Department Example 73.4 Factoring the Difference of Two Squares Factor:

7. Prepared by: David Crockett Math Department Example 73.5 Probability Without Replacement An urn contains 3 black marbles and 5 white marbles. A marble is drawn at random and replaced. Then a second marble is randomly drawn. (a) What is the probability that both marbles are black? (b) If the first marble is not replaced before the second marble is drawn, what is the probability that both marbles are black?

8. Prepared by: David Crockett Math Department Example 73.6 Probability Without Replacement An urn contains 4 red marbles and 7 blue marbles. Two marbles are drawn at random. What is the probability that the first is red and the second is blue if the marbles are drawn (a) with replacement? (b) without replacement? 2 5