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Lesson 9.5: Factoring Difference of Squares, page 500 Objectives: To factor binomials that are the difference of squares. To solve equations involving the differences of squares.

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Review of 9.3 & 9.4 Define factoring. How do we check our answer after factoring? Factor: A) k 2 – 11kh + 28h 2 B) 4x 2 + 2x - 6

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Review Multiply using FOIL: (x – 3) (x + 3). x 2 + 3x – 3x - 9 Answer: x 2 – 9 Remember: the outside/inside terms cancel b/c they are opposite terms. Multiply: (y + 2)(y – 2) Answer: y 2 – 4 This answer is a special case called the DIFFERENCE OF TWO SQUARES (a.k.a. DOTS).

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Factoring the Difference of Two Squares (DOTS) Clue 1: usually only 2 terms Clue 2: minus sign Clue 3: both terms are perfect squares General Form: x 2 – y 2 = (x + y)(x - y) MEMORIZE THESE PERFECT SQUARES: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256,…, 400,…,625,…900,…,10000

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Example 1: Factor each binomial. x 2 – y 2 = (x + y)(x - y) a) x 2 – 25b) 3a 2 – 48 c) 169x 2 – y 2 d) 81a 2 – 121b 2 Note: Always check for the GCF.

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e) m² - 64 f) 3b³ - 27b g) 16y² - 81z² h)

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Ex. 2: Apply several different factoring techniques. 1. 6x³ + 30x² - 24x - 120

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Ex. 3: Solve equations by factoring. 1. 4y² - 25 = 02. 17 – 68k² = 0

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3.4. 121a = 49a³

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Review Examples Factor Completely 1. 4x 2 – 12x 2. 12q 2 b +8qb 2 – 20q 3 b 2 3. 2am – 2bm – ap + bp 4. y 2 – 5y + 6 5. 10k 2 – 11kh + 3h 2 6. 64m 2 – 25n 2

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SUMMARY x 2 – y 2 = (x + y)(x - y) NBA #5, page 505, problems 16-42 even

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