Find the constant term in (x - 3/x^2)^9

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Using the binomial expansion: (a + b)^n = `sum` C(n,k) a^k*b^(n - k)

The expression given to us is: (x - 3/x^2)^9. n = 9, a = x and b = -3/x^2.

When a term in the series is constant, the power of x in the numerator and the power...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

Using the binomial expansion: (a + b)^n = `sum` C(n,k) a^k*b^(n - k)

The expression given to us is: (x - 3/x^2)^9. n = 9, a = x and b = -3/x^2.

When a term in the series is constant, the power of x in the numerator and the power of x in the denominator is the same. This is the case for k = 6, the numerator is x^6 and the denominator is  x^2^(9 - 6) = x^6.

The constant term is C(9, 3)*(-3)^(9 - 6)

= C(9, 3)*(-3)^3

= -27*9!/6!*3!

= -2268

The constant term is -2268

Approved by eNotes Editorial Team