Difference of Two Squares Chapter 5 Section 5.5

Objective Students will simplify products of the form (a + b)(a – b) and factor differences of two squares

Concept You now know how to use the FOIL method to multiply two binomials together 1. First 2. Outer 3. Inner 4. Last

Example (x + 2)(x – 2) (2x - 9y)(2x + 9y)

Concept (a + b)(a – b) = a2 – b2 (sum of two numbers) * (their differences) = (1st #2) – (2nd #2)

Concept If you cannot remember the rule you can always use the FOIL method. Using the rules allows less steps in solving the problem, you will not have to simplify at the end. Also the directions should help you determine what your answer will be (binomial)

Example (x + 3)(x – 3) (2x + 5)(2x – 5)

(a2 – 2b)(a2 + 2b) (xy + z2)(xy – z2) Example (a2 – 2b)(a2 + 2b) (xy + z2)(xy – z2)

Concept Working in the other direction, if you have the difference of two squares, you can factor the expression: a2 – b2 = (a + b)(a – b) Square root both the first term and last term, that will give you a and b

Example x2 – 49 16 – 9x2

Example 81a2 – 25x6 16x4 - 625

Questions

Assignment Worksheet