(2n +1)2 = 4n2 + 4n +1. I don’t know where the 4n comes from. This might be explained in a future chapter but I'm following the Study Organizer and it hasn't been covered yet.

Thanks for the explanation. Could you point me to where FOIL is covered in the Strategy Guides (Book and Chapter)? Thanks!

The explanation says that were are changing |x - 4| to -(x-4) because x -4 <=0. I don't see how we know x -4 <= 0.

I can see how we get to k2 = 4n^2 -4n + 1, using FOIL. But how do we factor to k = 4n(n-1)+1?

Can you explain why the fact that 6! and 41 do not share any prime factors makes 6!+41 a possible prime.

Why are we multiplying the remainder of x by 5 and then subtracting the remainder of y to get to 18.

How does 18=xy+y becomes 18=y(x+1)

I don’t understand how 4^a*(4^2) - 4^a - 4^a*(4^1) becomes 4^a*(4^2 - 4^0 - 4^1), since it seems to violate PEMDAS. Shouldn’t it instead become (4^a * 4^2) -4^a - (4^a * 4^1), since you are supposed to handle multiplication before subtraction?

I don’t understand how does a^b(1 - a^-1) becomes a^b-1(a - 1), and how does p(q + r) + s(q + r) becomes (p + s)(q + r)? Please also provide where is this explained in the guides.

How does (54 + m) + 0.20(54 + m) becomes 1.2(54 + m)? Where is this covered in the guides?