How do you factor #(a-b)^2 - 16(a+2b)^2#?

1 Answer
Sep 17, 2016

Answer:

#(a-b)^2-16(a+2b)^2 = -3(a+3b)(5a+7b)#

Explanation:

The difference of squares identity can be written:

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

Let #A=(a-b)# and #B=4(a+2b)#

Then we find:

#(a-b)^2-16(a+2b)^2 = (a-b)^2-(4(a+2b))^2#

#color(white)((a-b)^2-16(a+2b)^2) = ((a-b)-4(a+2b))((a-b)+4(a+2b))#

#color(white)((a-b)^2-16(a+2b)^2) = (a-b-4a-8b)(a-b+4a+8b)#

#color(white)((a-b)^2-16(a+2b)^2) = (-3a-9b)(5a+7b)#

#color(white)((a-b)^2-16(a+2b)^2) = -3(a+3b)(5a+7b)#