Expanding Exponent Expressions

[thomas49th]

Hi, I don know how to go about expanding things such as

3x\sqrt{3x-1}
apparently that equals 12x^{2} - 4x

i know that 3x\sqrt{3x-1} can be written as 3x(3x-1)^{\frac{1}{2}}

but i don't know what to do. I can't remeber.

Thanks :)

 

[Snazzy]

3x\sqrt{3x-1} \neq 12x^2 - 4x

 

[thomas49th]

SORRY MY BAD I MENT 2x\sqrt{3x-1} = 12x^{2} - 4x

How do i get there?

Thanks :)

 

[Snazzy]

2x\sqrt{3x-1} \neq 12x^2 - 4x

 

[thomas49th]

SORRY. Ill start a bit further back
i have this:

x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}

and I don't know how it simplifies to

\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}I can't see that the
x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}} will equal \frac{3x^{2}}{2\sqrt{3x-1}}

but i can't see how the other bit simplifies... can you show me

Thanks

 

[tiny-tim]

SORRY. Ill start a bit further back
i have this:

x^{2}\frac{3}{2}(2x-1)^{-1}{2} + 2x\sqrt{3x-1}

and I don't know how it simplifies to

\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}

I can't see that the
x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}} will equal \frac{3x^{2}}{2\sqrt{3x-1}}

Hi thomas49th!

Do you follow:

\frac{3x^{2}}{2\sqrt{3x-1}}\,+\,2x\sqrt{3x-1}

= \frac{3x^{2}}{2\sqrt{3x-1}}\,+\,\frac{2x(3x-1)}{\sqrt{3x-1}} ? ​

 

[thomas49th]

yes i can see a common denomitor so u multiply both the numerator and demonitor by 2\sqrt{3x-1} of the fraction
Cheerz :)