Factor completely
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 :)
Factor completely
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 :)
a^{2} ± 2ab + b^{2} = (a ± b)^{2}
a^{2} – b^{2} = (a + b)(a – b)
~~~~~~~~
a^{2} + 2ab – 63b^{2} =
a^{2} + 2ab + b^{2} – b^{2} – 63b^{2} =
(a^{2} + 2ab + b^{2}) – 64b^{2} =
(a + b)^{2} – (8b)^{2} =
(a + b + 8b)(a + b – 8b) =
(a + 9b)(a – 7b)