NP Chapter 2 Page 58 First Paragraph

[ray_serrano]

(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.

[esledge]

You may remember FOIL = First, Outer, Inner, Last, which is the reminder of terms to pair and multiply when distributing a factored expression.

(2n + 1)^2
= (2n + 1)(2n + 1)
= (2n)(2n) + (2n)(1) + (1)(2n) + (1)(1) (see pairings of First, Outer, Inner, Last?)
= 4n^2 + 2n + 2n + 1
= 4n^2 + 4n + 1

Looking back, you can now see that 4n is the sum of the Outer and Inner products. More generally, anything in this form follows this pattern: (a+b)^2 = a^2 + 2ab + b^2 = first term squared + 2*product of first and last + last term squared. We saw 4n because it is 2(2n)(1).

[ray_serrano]

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

[RonPurewal]

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

equations, inequalities, VIC guide
page 52