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Difference of Squares December 3, 2014 Pages 44 – 45 in Notes

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Warm-Up (Left Side – pg. 44) Find the square root of the following expressions: 1.9 2.25 3.x 2 4.x 4

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Objective solve quadratic equations and inequalities using graphs, tables, and algebraic methods.[8.D]

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Essential Question What skills that I have already learned will help me with finding the difference of squares?

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What is this method for factoring? If there are only 2 terms, check for difference of squares (2 terms that you can take the square root of). Factor like this… a 2 – b 2 = (a + b)(a – b) It will always factor into the sum times the difference of the square roots. *Always look for GCF first!

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Example 1 x 2 – 9 Is there a GCF? No. Remember: a 2 – b 2 = (a + b)(a – b) a = x and b = 3 So…factored form is… (x + 3)(x – 3)

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Example 2 16x 2 – 4y 2 Is there a GCF? Yes, 4. So divide both terms: 4(4x 2 – y 2 ) Factor inside the ( ) using: a 2 – b 2 = (a + b)(a – b) a = 2x and b = y So…factored form is… 4(2x + y)(2x – y)

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Example 3 25x 2 – 49y 2 Is there a GCF? No. Factor using: a 2 – b 2 = (a + b)(a – b) a = 5x and b = 7y So…factored form is… (5x + 7y)(5x – 7y)

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Example 4 5x 2 – 12 Is there a GCF? No. 5 is not a perfect square so it cannot be factored. This is called a “prime polynomial.” Prime

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Example 5 x 2 + 9 Addition of perfect squares can never be factored! Prime

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Example 6 x 4 – 16 Is there a GCF? No. Remember: a 2 – b 2 = (a + b)(a – b) a = x 2 and b = 4 So…factored form is… (x 2 + 4)(x 2 – 4) But the second binomial will factor again… (x 2 + 4)(x + 2)(x – 2) Completely factored

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Assignment – Difference of Squares 1.x 2 – 81 2.2x 2 – 8x 4 3.15x 2 – 225 4.x 2 – 25 5.8x 4 + 12x 2 6.14x 2 – 224y 2 7.x 2 + 4 8.9x 2 – 16y 2

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Reflection

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