factorisation (1 Viewer)

skillstriker · Feb 20, 2012

How does 3^2n-1 - 1 = (3ⁿ+1)(3ⁿ-1)
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It seems like the difference of 2 squares however I just can't work out how it factorises.

nightweaver066 · Feb 20, 2012

skillstriker said:
How does 3^2n-1 - 1 = (3ⁿ+1)(3ⁿ-1)
-------------------------------------------
It seems like the difference of 2 squares however I just can't work out how it factorises.

$3^{2n - 1} - 1$

$= \frac{3^{2n}}{3} - 1$

$= (\frac{3^n}{\sqrt{3}})^2 - 1$

$= (\frac{3^n}{\sqrt{3}} + 1)(\frac{3^n}{\sqrt{3}} - 1)$

Although i think you typed the LHS wrong.. so..

$3^{2n} - 1$

$= (3^n)^2 - 1 $, Can you see the two squares? Using indice laws, i can take out the squared like that to make it more clear for you$$

$= (3^n - 1)(3^n + 1)$

skillstriker · Feb 20, 2012

thanks so much!!! And yeah, i typed the question out wrong.

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factorisation (1 Viewer)

skillstriker

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