Difference of squares special case

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Difference of squares special case

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  1. Difference of Two Squares

    Slide 1 - Difference of Two Squares

    • Special Case!!!
  2. What you talkin’ ‘bout?!

    Slide 2 - What you talkin’ ‘bout?!

    • Sometimes, factoring the difference of two squares involves cases in which either or both squares are squares of polynomials.
    • In these cases, the expression may be factored using methods similar to what we did when we factored the difference of perfect squares.
    • 25a2 – (3a + 2b)2
  3. Examples:

    Slide 4 - Examples:

    • Factor:
    • 25a2 – (3a + 2b)2
    • One factor is 5a + (3a + 2b), and the other is 5a – (3a + 2b)
    • 5a + (3a + 2b) = 5a + 3a + 2b = 8a + 2b = 2(4a + b) (this is done because it’s prime)
    • 5a – (3a + 2b) = 5a – 3a - 2b = 2a - 2b = 2(a - b)
    • So, 25a2 – (3a + 2b)2 = 2(4a + b)2(a – b)
    • = 4(4a + b)(a – b) (Three factors)
  4. Example 2

    Slide 6 - Example 2

    • Factor:
    • (3a – 2b)2 – (2a – 5b)2
    • = [(3a – 2b) + (2a – 5b)][(3a – 2b) – (2a – 5b)]
    • = (3a – 2b + 2a – 5b)(3a – 2b – 2a + 5b)
    • = (5a – 7b)(a + 3b)