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factor completely. a^2+2ab-63b^2

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2 Answers

Hey Ben -- when we "eyeball" the final figure, what factors of -63 "offset" making +2?  Factors -3x21 too lopsided ... the -7x9 looks nice ... (a+9b)(a-7b) = a*a -7ab + 9ab -63b*b = a*a +2ab -63b*b ... Best wishes :) 

a2 ± 2ab + b2 = (a ± b)2
a2 – b2 = (a + b)(a – b)
~~~~~~~~
a2 + 2ab – 63b2 =
a2 + 2ab + b2 – b2 – 63b2 =
(a2 + 2ab + b2) – 64b2 =
(a + b)2 – (8b)2 =
(a + b + 8b)(a + b – 8b) =
(a + 9b)(a – 7b)