1. Section 5.6 Special Products of Binomials

2. 5.6 Lecture Guide: Special Products of Binomials Objective 1: Multiply by inspection a sum times a difference.

3. FactorsProducts 1. 2. 3. 4. Multiply each pair of factors. See if you can observe a pattern as you form the products. Example: 5. Can you describe what you observed?

4. Algebraically Verbally This product of a sum times a difference is the ____________ of their squares. Algebraic Example _______________ Sum Times a Difference:

5. FactorsProducts 6. 7. 8. 9. Use the pattern for a sum times a difference to multiply each pair of factors. Example:

6. FactorsProducts 10. 11. 12. 13. 14. Use the pattern for a sum times a difference to multiply each pair of factors.

7. Objective 2: Determine the square of a binomial by inspection. FactorsProducts 15. 16. 17. 18. Multiply each pair of factors. See if you can observe a pattern as you form the products. Example:

8. Algebraically Square of a Sum Verbally A trinomial that is the square of a binomial has: 1. a first term that is a _________ of the first term of the binomial. 2. a middle term that is ______________ the product of the two terms of the binomial. 3. a last term that is a ______________ of the last term of the binomial. Algebraic Example Square of a Sum and Square of a Difference Square of a Difference

9. FactorsProducts 19. 20. 21. 22. 23. 24. 25. Use the patterns for a square of a sum and the square of a difference to multiply each pair of factors. Example:

10. One reason for practicing the multiplication of special products is to recognize these products when factoring. Select the correct factored form for each polynomial to complete each statement. 26. 27. 28. 29. A. B. C. D. E. F.

11. Objective 3: Use the order of operations to simplify polynomials. Order of Operations Step 1: Start with the expression within the innermost pair of grouping symbols. Step 2: Perform all exponentiations. Step 3: Perform all multiplications and divisions as they appear from left to right. Step 4: Perform all additions and subtractions as they appear from left to right.

12. Use the correct order of operations to simplify each polynomial. 30. (a) (b)

13. Use the correct order of operations to simplify each polynomial. 31. (a) (b)

14. Use the correct order of operations to simplify each polynomial. 32.

15. Use the correct order of operations to simplify each polynomial. 33.

16. 34. Subtract the square of from the square of.

17. 35. Expand: Factor:

18. 36. Expand: Factor: