<s>[INST] Expanding $(2y-2)^2$ by FOIL Expanding $(2y-2)^2$
Isn't this same as $$(2y-2)(2y-2)\ ?$$
$$4y^2-6y+4$$
This should be FOILd shouldn't it?
 [/INST] Yes, $(2y-2)^2=(2y-2)(2y-2)$.  
FOILing should work, but will get you $4y^2−8y+4$, rather than $4y^2−6y+4$, as shown:
$(2y-2)(2y-2)=(2y)(2y)+(2y)(-2)+(-2)(2y)+(-2)(-2)$ 
$=4y^2-4y-4y+4=4y^2−8y+4$
If you want to memorize the formula which will get you the same result, it is
$$(a+b)^2=a^2+2ab+b^2$$
In your example, $a=2y$ and $b=-2$, so you get
$$(2y)^2+2(2y)(-2)+(-2)^2=4y^2-8y+4$$
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