Difference of squares special case

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Slide 1  Difference of Two Squares
 Special Case!!!

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

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)

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)