# simplifying algebraic expressions

• Jul 21st 2010, 11:34 PM
mastermin346
simplifying algebraic expressions
express $\displaystyle 3^{n+2}-3^{n}+10(3^{n-1})$ in the simplest form.
• Jul 21st 2010, 11:43 PM
pencil09
Quote:

Originally Posted by mastermin346
express $\displaystyle 3^{n+2}-3^{n}+10(3^{n-1})$ in the simplest form.

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

-- hope it'll help --
(pertamax euy...)
• Jul 22nd 2010, 12:01 AM
bigwave
$\displaystyle 3^{n+2}-3^{n}+10(3^{n-1}) \Rightarrow 3^{n}3^{2}-3^{n}+10(3^n3^{-1})$

so

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

now combine like terms

$\displaystyle \frac{34}{3}3^n$
• Jul 22nd 2010, 02:17 AM
Prove It
Quote:

Originally Posted by bigwave
$\displaystyle 3^{n+2}-3^{n}+10(3^{n-1}) \Rightarrow 3^{n}3^{2}-3^{n}+10(3^n3^{-1})$

so

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

now combine like terms

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

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