How do you factor #u^2-2u+1-v^2#?

1 Answer
Sep 2, 2016

Answer:

#u^2-2u+1-v^2=(u-v-1)(u+v-1)#

Explanation:

The difference of squares identity can be written:

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

Use this with #a=(u-1)# and #b=v# as follows:

#u^2-2u+1-v^2=(u-1)^2-v^2#

#color(white)(u^2-2u+1-v^2)=((u-1)-v)((u-1)+v)#

#color(white)(u^2-2u+1-v^2)=(u-1-v)(u-1+v)#

#color(white)(u^2-2u+1-v^2)=(u-v-1)(u+v-1)#