How do you factor #x^2-4x-4#?

1 Answer
Aug 27, 2017

#x^2-4x-4 = (x-2-2sqrt(2))(x-2+2sqrt(2))#

Explanation:

We can factor this by completing the square and using the difference of squares identity:

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

with #a=(x-2)# and #b=2sqrt(2)# as follows:

#x^2-4x-4 = x^2-4x+4-8#

#color(white)(x^2-4x-4) = (x-2)^2-(2sqrt(2))^2#

#color(white)(x^2-4x-4) = ((x-2)-2sqrt(2))((x-2)+2sqrt(2))#

#color(white)(x^2-4x-4) = (x-2-2sqrt(2))(x-2+2sqrt(2))#