How do you factor #48x^2 + 16x - 16#?

1 Answer
George C.
Sep 14, 2016

#48x^2+16x-16 = 4/3(6x+1-sqrt(13))(6x+1+sqrt(13))#

Explanation:

The difference of squares identity can be written:

#a^2-b^2=(a-b)(a+b)#

Use this with #a=(6x+1)# and #b=sqrt(13)# as follows:

#48x^2+16x-16 = 4/3(36x^2+12x-12)#

#color(white)(48x^2+16x-16) = 4/3(36x^2+12x+1-13)#

#color(white)(48x^2+16x-16) = 4/3((6x+1)^2-(sqrt(13))^2)#

#color(white)(48x^2+16x-16) = 4/3((6x+1)-sqrt(13))((6x+1)+sqrt(13))#

#color(white)(48x^2+16x-16) = 4/3(6x+1-sqrt(13))(6x+1+sqrt(13))#

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