How do you factor the expression # x² - 4x + 4#?

1 Answer
George C.
Mar 1, 2016

This is a perfect square trinomial:

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

Explanation:

In the general case we have:

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

By reversing the sign on #b# we can also write:

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

So if the first and last terms of a trinomial are both squares, just check that the middle one is #+-# twice the product of the square roots of those terms. If it is then you have a perfect square trinomial.

In our example, #a=x# and #b=-2#, giving:

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

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