How do you factor #x^2-4x+4# using the perfect squares formula?

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Answer 1 · 2017-05-03T13:59:18

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

I think what is being referred to is the relationship:

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

We've been given the equation #x^2-4x+4# - let's factor using the above relationship.

We can take the #x^2# term and therefore assign #x=a#. We can also see that the #+4# can be assigned to the #b^2# term, giving #b=pm2#.

Lastly, we can take the #-4x# term, assign it to the #+2ab# and say:

#-4x=2ab#

#-2x=ab#

We can substitute #x# in for #a#:

#-2x=xb#

#-2=b#

and this tells us we will use #b=-2# and not #b=2#.

All in all, we'll get:

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