How do you factor completely #a^2 - 4b^2 - 4a + 4#?

1 Answer
George C.
Sep 2, 2016

#a^2-4b^2-4a+4 = (a-2b-2)(a+2b-2)#

Explanation:

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

We use this with #A=(a-2)# and #B=2b# as follows:

#a^2-4b^2-4a+4 = (a^2-4a+4)-4b^2#

#color(white)(a^2-4b^2-4a+4) = (a-2)^2-(2b)^2#

#color(white)(a^2-4b^2-4a+4) = ((a-2)-2b)((a-2)+2b)#

#color(white)(a^2-4b^2-4a+4) = (a-2b-2)(a+2b-2)#

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