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Factoring

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afvatcha
 Post subject: Factoring
 Post Posted: Tue May 05, 2009 9:20 pm 
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Course Students


Posts: 34
What would(a-b)^4 look like completely factored.

I assumed it would be (a-b)(a+b)(a-b)(a+b).

Where did I go wrong???
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RonPurewal
 Post subject: Re: Factoring
 Post Posted: Wed May 06, 2009 3:46 pm 
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ManhattanGMAT Staff


Posts: 7146
afvatcha wrote:
What would(a-b)^4 look like completely factored.

I assumed it would be (a-b)(a+b)(a-b)(a+b).

Where did I go wrong???


nope. that would be (a^2 - b^2) squared, which doesn't work out to a^4 - b^4. try multiplying it out if you don't see this.

--

you CAN use the difference of squares formula, since a^4 is the square of a^2 and b^4 is the square of b^2. therefore, your pattern factors into
(a^2 - b^2)(a^2 + b^2)

now, the first of these is the traditional difference of squares. the second, however, doesn't factor, at all, into anything.

so we have the final product:
(a - b)(a + b)(a^2 + b^2)
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chintanjpatel
 Post subject: Re: Factoring
 Post Posted: Sat May 09, 2009 2:59 pm 
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Students


Posts: 11
can we write (a-b)^2 = a^2 - B^2. i guess not. so how can we write (a-b)^4= (a^2-b^2)^2.
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StaceyKoprince
 Post subject: Re: Factoring
 Post Posted: Fri May 15, 2009 2:35 pm 
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ManhattanGMAT Staff


Posts: 6064
Location: San Francisco
Chintan, I'm not quite sure from you're wording, but I think when you say "how can we write..." you're saying that you know that we can't actually do it. If you're actually asking how we can write that, let me know.

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