Problem Following Along Algebra Steps

Question

I have been given a question with the solution. However I am having trouble following the maths steps that have been taken in the solution. I'm unsure how they have gotten from step 1 to step 2, shown below:

EDIT... Note that there are two completely different variables here, $Vgs$ and $Vt$.

$ Step 1... \ 7 = Vgs + 5 ( Vgs - Vt ) ^2 $

$ Step 2... \ 7 = Vgs + 5 ( Vgs^2 - 2VgsVt + Vt^2 ) $

Thanks for any help.

Answer 1

If V, g and s are different variables or g, s and t are subscripts, Vgs - Vt squared equals (Vgs - Vt)(Vgs - Vt), which was expanded to (Vgs)(Vgs) - 2(Vgs)(Vt) + (Vt)(Vt)= Vgs^2 - 2VgsVt + Vt^2.

Answer 2

Looks like the variables are $V_{gs}$ and $V_{t}$, that is: $gs$ and $t$ are subscripts and not multiplied with $V$.

In that case:

$$(V_{gs} - V_{t})^2 = V_{gs}^2 - 2V_{gs}V_{t} + V_{t}^2$$

Which is a very well known binomial expansion.