Asked by Spenser

Find the constant term or the term independent of x in the expansion of (3x – 5/x to the 2nd power )and to the 9th power

Answered by drwls
(3x - 5/x)^2 = 9x^2 -30 + 25/x^2

The constant term is -30.

Do the multiplication by (3x - 5/x) eight more times for the second part of your question.
Answered by Reiny
In the expansion of (3x - 5/x)^n
there is no term independent of x, (a constant term), if n is odd, in your case 9

the general term would be C(9,r)(3x)<sup>r</sup>(-5/x)<sup>9-r</sup>
=C(9,r)(3)<sup>r</sup> (-5)^<sup>-r</sup>x<sup>r-9</sup>
=C(9,r)(3)<sup>r</sup>(-5)<sup>9-r</sup>x<sup>2r-9</sup>

so 2r-9 = 0 for the x to drop out
but r has to be a whole number, so there is no solution
Answered by Spenser
Where did you get -30 from?

to drwls
Answered by spenser
thz i am done wit this
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