Difference of two squares

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Difference of two squares

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  1. Difference of Two Squares

    Slide 1 - Difference of Two Squares

  2. Recognizing:

    Slide 2 - Recognizing:

    • a2 – b2
    • This can be expressed as the product of two factors.
    • One factor is the sum of the square roots of both terms (a + b)
    • The other factor is the difference of the same (a – b)
    • a2 – b2 = (a + b)(a – b)
    • Note: the way this works in reverse is because the middle terms add to zero (0).
  3. Factoring:

    Slide 3 - Factoring:

    • Find the square roots of the two terms.
    • Make their sum one factor and subtract the second from the first for the other factor.
    • Example:
    • 18c2 – 50
    • = 2(9c2 – 25)
    • = 2[(3c)2 – 52]
    • = 2(3c + 5)(3c – 5)
  4. Example cont…

    Slide 4 - Example cont…

    • Example 2:
    • x4 – y4
    • = (x2 + y2)(x2 – y2)
    • = (x2 + y2)(x + y)(x – y)