simplifying algebraic expressions

**mastermin346** · July 21st 2010, 11:34 PM

express $3^{n+2}-3^{n}+10(3^{n-1})$ in the simplest form.

**pencil09** · July 21st 2010, 11:43 PM

Originally Posted by mastermin346

express $3^{n+2}-3^{n}+10(3^{n-1})$ in the simplest form.

$3^{n+2}-3^{n}+10(3^{n-1})= 3^n 3^2-3^{n}+10(3^n) (3^{-1})$
$3^{n+2}-3^{n}+10(3^{n-1})= 3^n (3^2-1+10(3^{-1}))$

-- hope it'll help --
(pertamax euy...)

**bigwave** · July 22nd 2010, 12:01 AM

$3^{n+2}-3^{n}+10(3^{n-1})<br /> \Rightarrow<br /> 3^{n}3^{2}-3^{n}+10(3^n3^{-1})$

so

$9(3^{n})-3^{n}+\frac{10}{3}(3^n)$

now combine like terms

$\frac{34}{3}3^n$

**Prove It** · July 22nd 2010, 02:17 AM

Originally Posted by bigwave

$3^{n+2}-3^{n}+10(3^{n-1})<br /> \Rightarrow<br /> 3^{n}3^{2}-3^{n}+10(3^n3^{-1})$

so

$9(3^{n})-3^{n}+\frac{10}{3}(3^n)$

now combine like terms

$\frac{34}{3}3^n$

Surely $\frac{34}{3}\cdot 3^n = 34 \cdot 3^{n - 1}$ is simpler...

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