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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) k2 – 11kh + 28h2 B) 4x2 + 2x - 6

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**DIFFERENCE OF TWO SQUARES**

Review Multiply using FOIL: (x – 3) (x + 3). x2 + 3x – 3x - 9 Answer: x2 – 9 Remember: the outside/inside terms cancel b/c they are opposite terms. Multiply: (y + 2)(y – 2) Answer: y2 – 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: x2 – y2 = (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. x2 – y2 = (x + y)(x - y)**

a) x2 – 25 b) 3a2 – 48 c) 169x2 – y2 d) 81a2 – 121b2 Note: Always check for the GCF.

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m² - 64 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.**

– 68k² = 0

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3. a = 49a³

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**Review Examples Factor Completely**

4x2 – 12x 12q2b +8qb2 – 20q3b2 2am – 2bm – ap + bp y2 – 5y + 6 10k2 – 11kh + 3h2 64m2 – 25n2

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SUMMARY x2 – y2 = (x + y)(x - y) NBA #5, page 505, problems even

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