Factor completely

## 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 :)

*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)**