1. Copyright © 2013, 2009, 2006 Pearson Education, Inc.
Section 5.3
Special Products
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

3. Special Products
In this section we will use the distributive property to develop patterns that will allow us to multiply some special binomials quickly.
We will find the product of two binomials using a method called FOIL.
We will learn a formula for finding the square of a binomial sum. We will also learn formula for finding the product of the sum and difference of two terms.

4. Using the FOIL Method to Multiply Binomials
Multiplying Polynomials - FOIL
Using the FOIL Method to Multiply Binomials
last F O I L
first
inside
Product of First terms
Product of Outside terms
Product of Inside terms
Product of Last terms
outside

5. Multiplying Polynomials - FOIL
EXAMPLE
Multiply
SOLUTION
last F O I L
first
Multiply
inside
outside
Combine like terms

6. FOIL Method Multiply: (5x + 2)(x + 7)
EXAMPLE F O I L
(5x + 2)(x + 7) = 5x·x + 5x·7 + 2·x + 2·7
=5x2 + 35x + 2x +14
=5x2 + 37x +14
Product of the last terms
Product of the first terms
Product of the outside terms
Product of the inside terms

7. FOIL Method Multiply: (5x + 2)(x + 7)
EXAMPLE F O I L
(5x + 2)(x + 7) = 5x·x + 5x·7 + 2·x + 2·7
=5x2 + 35x + 2x +14
=5x2 + 37x +14
Product of the last terms
Product of the first terms
Product of the outside terms
Product of the inside terms

8. Objective #1: Example

9. Objective #1: Example

10. Objective #1: Example

11. Objective #1: Example

13. Multiplying the Sum and Difference of Two Terms
(A + B)(A – B) = A2 – B2
The product of the sum and the difference of the same two terms is the square of the first term minus the square of the second term.

14. Objective #2: Example

15. Objective #2: Example

16. Objective #2: Example

17. Objective #2: Example

19. The Square of a Binomial Sum
(A + B)2 = A2 + 2AB + B2
The square of a binomial sum is the first term squared plus two times the product of the terms plus the last term squared.

20. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
Use the special-product formula shown. +
= Product

21. Objective #3: Example

22. Objective #3: Example

23. Objective #3: Example

24. Objective #3: Example

26. The Square of a Binomial Difference
(A – B)2 = A2 – 2AB + B2
The square of a binomial difference is the first term squared minus two times the product of the terms plus the last term squared.

27. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
Use the special-product formula shown. – +
= Product

28. Objective #4: Example

29. Objective #4: Example

30. Objective #4: Example

31. Objective #4: Example

32. Multiplying Polynomials – Special Formulas
The Square of a Binomial Sum
The Square of a Binomial Difference
The Product of the Sum and Difference of Two Terms