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

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.

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

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

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

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

Objective #1: Example

Objective #1: Example

Objective #1: Example

Objective #1: Example

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.

Objective #2: Example

Objective #2: Example

Objective #2: Example

Objective #2: Example

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.

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

Objective #3: Example

Objective #3: Example

Objective #3: Example

Objective #3: Example

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.

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

Objective #4: Example

Objective #4: Example

Objective #4: Example

Objective #4: Example

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