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I'm having trouble making sense of this.

Again why does:

$$10^{k} - 10^{k - 1} = 9 \cdot 10^{k - 1}$$

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1  
factor $10^{k-1}$ out of $10^k-10^{k-1}$ –  anon Jan 17 at 2:43
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Try factoring out $10^{k-1}$. –  user121926 Jan 17 at 2:43
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Write $10^k = 10\cdot 10^{k-1}$ then factor out $10^{k-1}$ –  Bill Dubuque Jan 17 at 2:43
    
Hi! You can factor a $10^{k-1}$ out of the LHS. HTH! –  enthdegree Jan 17 at 2:46

2 Answers 2

up vote 4 down vote accepted

$10^k-10^{k-1}=10^{k-1}(10-1)=9\cdot10^{k-1}$

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Factoring $10^k-10^{k-1}=10^{k-1}(10-1)$.

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