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Factoring question

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Factoring question [#permalink] New post 11 Sep 2007, 07:24
Factors are my weakness, so if this is elementary please forgive me...

Question:

A^2 + B^2 + 2AB = 9

What is A+B?


The steps in explanation goes as follows: "Factor the expression A^2 + B^2 + 2AB. Then Unsquare both sides, taking both the positive and negative roots into account"

Step 1. (A+B)^2 = 9

Answer: 2. A+B = 3 or A +B = -3

My question is what happened to the + 2AB in Step 1?


Thanks in advance.
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Re: Factoring question [#permalink] New post 11 Sep 2007, 08:04
boggin wrote:
Factors are my weakness, so if this is elementary please forgive me...

Question:

A^2 + B^2 + 2AB = 9

What is A+B?


The steps in explanation goes as follows: "Factor the expression A^2 + B^2 + 2AB. Then Unsquare both sides, taking both the positive and negative roots into account"

Step 1. (A+B)^2 = 9

Answer: 2. A+B = 3 or A +B = -3

My question is what happened to the + 2AB in Step 1?


Thanks in advance.



Yes, it's a basic question.

We have a formula:

(A+B)^2 = A^2 + B^2 + 2AB

Reverse is also true..i.e:

A^2 + B^2 + 2AB = (A+B)^2

In your question,

A^2 + B^2 + 2AB = 9
=> (A+B)^2 = 9 (since A^2 + B^2 + 2AB = (A+B)^2)
=> (A+B) = Sqrt(9)
=> (A+B) = +3 or -3

Hope it's clear now.

- Brajesh

Last edited by b14kumar on 11 Sep 2007, 08:41, edited 1 time in total.
Intern
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Joined: 11 Oct 2006
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Thanks [#permalink] New post 11 Sep 2007, 08:30
Thanks for the quick reply, guess Its obvious I need to memorize those formulas
Thanks   [#permalink] 11 Sep 2007, 08:30
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