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# Distributed Form to Factored Form

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

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

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Re: Distributed Form to Factored Form  [#permalink]

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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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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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16 May 2011, 20:31
a^b = 2^3

a^(b-1) = 2^2

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

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

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