Difference of two squares

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Slide 1  Difference of Two Squares

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).

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)

Slide 4  Example cont…
 Example 2:
 x4 – y4
 = (x2 + y2)(x2 – y2)
 = (x2 + y2)(x + y)(x – y)