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NP Chapter 2 Page 58 First Paragraph

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ray_serrano
 Post subject: NP Chapter 2 Page 58 First Paragraph
 Post Posted: Sat Apr 18, 2009 7:42 am 
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Course Students


Posts: 10
(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.
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esledge
 Post subject: Re: NP Chapter 2 Page 58 First Paragraph
 Post Posted: Mon Apr 20, 2009 1:16 pm 
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ManhattanGMAT Staff


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Location: St. Louis, MO
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).

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ManhattanGMAT
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ray_serrano
 Post subject: Re: NP Chapter 2 Page 58 First Paragraph
 Post Posted: Tue Apr 21, 2009 8:42 am 
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Course Students


Posts: 10
Thanks for the explanation. Could you point me to where FOIL is covered in the Strategy Guides (Book and Chapter)? Thanks!
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RonPurewal
 Post subject: Re: NP Chapter 2 Page 58 First Paragraph
 Post Posted: Sun May 03, 2009 4:27 am 
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ManhattanGMAT Staff


Posts: 7146
ray_serrano wrote:
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
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