Calculus

Find the coefficient of the x^2 term in the expansion of (3x - (2/x^2))^8

  1. 👍
  2. 👎
  3. 👁
  1. I would advice to take out the 1/x^2 term first:

    (3x - (2/x^2))^8 =

    1/x^16 (3 x^3 - 2)^8 =

    So you need to get x^18 from the expansion of the bracket:

    (3 x^3 - 2)^8 contains a term:

    (3 x^3)^6 (-2)^2 Binomial(8,6)

    So, the coefficient is 81648.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the coefficient of x^4y^3 in the expansion of (x+2y)^7

  2. Math

    Find the middle term in the expansion of (2x+3y)^12

  3. Physics

    Wine bottles are never completely filled: a small volume of air is left in the glass bottle's cylindrically shaped neck (inner diameter d = 18.5mm) to allow for wine's fairly large coefficient of thermal expansion. The distance H

  4. math

    Consider the expansion of (x + 2)11. (a) Write down the number of terms in this expansion. (b) Find the term containing x2.

  1. Math

    find the third term in the expansion of (3x-y)^6

  2. same type of binomial theorem question

    Question: Find the first 3 terms in the expansion, in ascending powers of x, of (2 + x)^6. Hence, obtain the coefficient of x^2 in the expansion of (2 + x - x^2)^6 I know the first part of the question, and the first 3 terms are

  3. Math

    Find the coefficient of x^5y^7 in the expansion of (5x+2y)^12 12 (x)^5 (2y)^7 3 My answer which i got wrong is 220x^5(128y^7)= 28160x^5y^7

  4. Physics

    A 3.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 52.0°C, how much gasoline spills out? [Hint: Be sure to account for the expansion

  1. Math - binomial

    Find the indicated term in the expansion of the given binomial. The term that does not contain x in the expansion of (6x+1/2x)^12 Is there an easier way to find the answer instead of going through finding 13 terms Thanks.

  2. math

    The 3rd term of a geometric progression is nine times the first term.if the second term is one-twenty fourth the 5th term.find the 4th term. solution ar^2=9a r=sqr of 9 r=3.pls help me on how to get the first term(a)

  3. physics

    An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can’s initial volume at 8 °C is 4.8 × 10-4 m3. The coefficient of volume expansion for

  4. algebra

    Match the term with the definition. 1. a number without a variable Examples: 1, 5, -9 a. constant b. like terms c. term d. coefficient e.expression 2. a collection of terms and constants separated by addition or subtraction

You can view more similar questions or ask a new question.