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How can you get $10^{n+1}$ from $9\cdot 10^n+10^n$? This is part of a proof I am working on.

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    **Hint** $\ $ Multiply $\: 10\ =\ 9 + 1\: $ by $\:10^n$2012-03-01

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Start with the distributive law.

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    Wow I totally did not think of that. I thought it would be much more difficult. Thanks!2012-03-01
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$\begin{aligned} 9 \cdot 10^n + 10^n &= (10-1) \cdot 10^n + 10^n \\ &= 10 \cdot 10^n - 10^n + 10^n \\ &= 10^{n+1} \end{aligned}$

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    Another way is $9 \cdot 10^n + 10^n = (9 + 1) \cdot 10^n = 10 \cdot 10^n = 10^{n+1}$.2012-03-02