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

(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.

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)r(-5/x)9-r
=C(9,r)(3)r (-5)^-rxr-9
=C(9,r)(3)r(-5)9-rx2r-9

so 2r-9 = 0 for the x to drop out
but r has to be a whole number, so there is no solution

Where did you get -30 from?

to drwls

thz i am done wit this

To find the constant term in the expansion of (3x – 5/x)^2, we can use the binomial theorem. According to the binomial theorem, the constant term can be found by raising the coefficient of x and the constant term to the power equal to the exponent.

In this case, the coefficient of x is 3 and the constant term is -5/x. The exponent is 2. Using the binomial theorem formula, the constant term can be calculated as follows:

Constant term = coefficient of x^0 * (constant term of -5/x)^(2-0)

Since any term with x in the denominator raised to a positive power will cancel out the x in the numerator, we can simplify the expression:

Constant term = (1) * (-5/x)^(2)

Simplifying further, we get:

Constant term = -25/x^2

Now, let's find the constant term in the expansion of (3x – 5/x)^9. Following the same logic as above:

Constant term = coefficient of x^0 * (constant term of -5/x)^(9-0)

(Constant term of -5/x)^(9-0) is simply (-5/x)^9.

Constant term = (1) * (-5/x)^9

Simplifying further, we get:

Constant term = -1953125/x^9

Therefore, the constant term in the expansion of (3x – 5/x)^2 is -25/x^2, and the constant term in the expansion of (3x – 5/x)^9 is -1953125/x^9.