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Expanding $(2y-2)^2$

Isn't this same as $(2y-2)(2y-2)\ ?$

$4y^2-6y+4$

This should be FOILd shouldn't it?

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    What on earth is FOIL???2011-10-31

1 Answers 1

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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

$(2y)^2+2(2y)(-2)+(-2)^2=4y^2-8y+4$