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

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.

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

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

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

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

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

Objective #1: Example

Objective #1: Example

Objective #1: Example

Objective #1: Example

Objective #1: Example

Objective #1: Example

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

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

Objective #2: Example

Objective #2: Example

Objective #2: Example

Objective #2: Example

Objective #2: Example

Objective #2: Example

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

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,

Objective #3: Example

Objective #3: Example

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

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

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

Objective #4: Example

Objective #4: Example

Objective #4: Example

Objective #4: Example