1. Copyright © 2013, 2009, 2006 Pearson Education, Inc.
Section 5.5
Factoring
Special Forms
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

3. The Difference of Two Squares
If A and B are real numbers, variables, or algebraic expressions, then
In words: The difference of the squares of two terms, factors as the product of a sum and a difference of those terms.

4. The Difference of Two Squares
EXAMPLE
Factor:
SOLUTION
We must express each term as the square of a monomial. Then use the formula for factoring
Express as the difference of two squares
Factor using the Difference of Two Squares method

5. The Difference of Two Squares
EXAMPLE
Factor:
SOLUTION
The GCF of the two terms of the polynomial is 6. We begin by factoring out 6.
Factor the GCF out of both terms
Factor using the Difference of Two Squares method

6. The Difference of Two Squares
EXAMPLE
Factor completely:
SOLUTION
Express as the difference of two squares
The factors are the sum and difference of the expressions being squared
The factor is the difference of two squares and can be factored

7. The Difference of Two Squares
CONTINUED
The factors of are the sum and difference of the expressions being squared
Thus,

8. Factoring Completely Factor completely:
EXAMPLE
Factor completely:
SOLUTION
Group terms with common factors
Factor out the common factor from each group
Factor out x + 3 from both terms
Factor as the difference of two squares

9. Objective #1: Example

10. Objective #1: Example

11. Objective #1: Example

12. Objective #1: Example

13. Objective #1: Example

14. Objective #1: Example

16. Factoring Perfect Square Trinomials
Factoring Special Forms
Factoring Perfect Square Trinomials
Let A and B be real numbers, variables, or algebraic expressions.

17. Factoring Perfect Square Trinomials
EXAMPLE
Factor:
SOLUTION
Express in form
Factor

18. Objective #2: Example

19. Objective #2: Example

20. Objective #2: Example

21. Objective #2: Example

22. Objective #2: Example

23. Objective #2: Example

25. Grouping & Difference of Two Squares
EXAMPLE
Factor:
SOLUTION
Group as minus a perfect square trinomial to obtain a difference of two squares
Factor the perfect square trinomial
Rewrite as the difference of two squares

26. Grouping & Difference of Two Squares
CONTINUED
Factor the difference of two squares. The factors are the sum and difference of the expressions being squared.
Simplify
Thus,

27. Objective #3: Example

28. Objective #3: Example

30. Factoring the Sum & Difference of Two Cubes
Factoring the Sum of Two Cubes
Same Signs Opposite Signs
2) Factoring the Difference of Two Cubes

31. The Sum & Difference of Two Cubes
EXAMPLE
Factor:
SOLUTION
Rewrite as the Sum of Two Cubes
Factor the Sum of Two Cubes
Simplify
Thus,

32. The Sum & Difference of Two Cubes
EXAMPLE
Factor:
SOLUTION
Rewrite as the Difference of Two Cubes
Factor the Difference of Two Cubes
Simplify
Thus,

33. Objective #4: Example

34. Objective #4: Example

35. Objective #4: Example

36. Objective #4: Example