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Distributed Form to Factored Form

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Intern
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Joined: 11 May 2011
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Distributed Form to Factored Form  [#permalink]

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New post 16 May 2011, 17:15
How does \(a^b-a^b^-^1\) become \(a^b^-^1(a-1)\)?

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Director
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Re: Distributed Form to Factored Form  [#permalink]

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New post 16 May 2011, 17:45
\(a^b - a ^(b-1)\)
Taking a^(b-1) common we have

\((a^(b-1))*(a-1)\)
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Re: Distributed Form to Factored Form  [#permalink]

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New post 16 May 2011, 18:34
napy27 wrote:
How does \(a^b-a^b^-^1\) become \(a^b^-^1(a-1)\)?


Think of it in the following way:

\(3^5 - 3^4 = 3^4*3^1 - 3^4 = 3^4 ( 3^1 - 1)\)

b is 5 and (b-1) is 4. You can take the smaller power common out of the two terms.

Similarly,
\(3^7 - 3^4 = 3^4 ( 3^3 - 1)\)
or
\(a^b - a^{b-3} = a^{b-3} (a^3 - 1)\)

Try revising the rules of exponents to gain confidence in this topic.
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Re: Distributed Form to Factored Form  [#permalink]

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New post 16 May 2011, 20:31
a^b = 2^3

a^(b-1) = 2^2

2^3 - 2^2 = 2^2(2-1)

hence the answer.

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Re: Distributed Form to Factored Form &nbs [#permalink] 16 May 2011, 20:31
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