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

Question

Factor completely

Answer 1

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 :) 

Answer 2

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)