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Explanation of the square of Binomials?
Well, I am not sure if I can really help but based on what I have learned, this is the explanation:

it can also be written like this
(x-2) (x-2)
And you can multiply them using your preferred method.

             -2x+ 4
But because we are taught to do the shortcut way, it is explained to do it like this:
1.) Square the first term.
2.) Multiply the first term and the second term, double their product after..
3.) Square the second term.
4.) Connect you answers together.(don't forget their signs)
=x^2-4x+4(if I am not mistaken)