Use the following expansion to find the following (x

We'll use the formula of general term of binomial
expansion (a+b)^n:

T(k+1) =
C(n,k)*[a^(n-k)]*b^k

Let a = x, b = -3/x^2, n =
9

T(k+1) =
C(9,k)*[x^(9-k)]*[(-3/x^2)^k]

This term must contain x^6,
therefore we'll consider just the power of x.

We'll use the
negative power property:

(1/x^2)^k =
x^(-2k)

x^(9-k)*x^(-2k) =
x^6

We'll add the exponents from the left
side:

x^(9-k-2k) = x^6

Since
the bases both sides are matching, we'll equate the
exponents:

9-3k = 6

We'll
divide by 3:

3 - k = 2

We'll
keep k to the left side and we'll subtract 3 both sides:

-k
= -3 + 2

-k = -1

k =
1

Since k = 1, therefore the second term of
the expansion, T2, will contain x^6.