Author Topic: mtwtfss methods questions (Read 890 times) Tweet Share

mtwtfss · « **on:** December 02, 2008, 10:06:34 am »

Just a quick one, because the book offers a pretty poor example...

Find and evaluate the term that is independent of x in the expansion of (3x+2/x^2)^6.

Thanks.

mtwtfss · « **Reply #1 on:** December 02, 2008, 02:49:35 pm »

And could someone explain how to divide -2x into x^5 etc.. In this question:

-2x+3/x^5+0x^4+3x^3-4x^2+6x-8

I know how to these generally; however, I've got no idea how to divide -2x into x^5 and so on.

plato · « **Reply #2 on:** December 02, 2008, 09:47:32 pm »

plato · « **Reply #3 on:** December 02, 2008, 10:21:50 pm »

Quote from: mtwtfss on December 02, 2008, 10:06:34 am

Just a quick one, because the book offers a pretty poor example...

Find and evaluate the term that is independent of x in the expansion of (3x+2/x^2)^6.

Thanks.

I think you are asking for the expansion of $(3x+\frac{2}{x^2})^6$

This is similar to expanding $(a+b)^6 = 6C0 \times a^6b^0+6C1 \times a^5b^1+6C2 \times a^4b^2+....$
Sorry, I can't find the LaTex code for Combinations.

Anyway, it is the term $6C2 \times a^4b^2$ that you want if you let $a=3x$ and $b = \frac{2}{x^2}$

Then
$6C2 \times a^4b^2$ becomes $6C2 \times (3x)^4\times (\frac{2}{x^2})^2$

You will note that this will reduce to a number without any x's in it.

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