Math

posted by .

Expand [1+x^2(1+x)]^7 in ascending powers of x as the term in x^8.

  • Math -

    Use binomial expansion over and over again

  • Math -

    let u = x^2(1+x)
    then [1 + x^2(1+x)]^7 = (1+u)^7
    = 1 + 7u + 21u^2 + 35u^3 + 35u^4 + 21u^5 + 7u^6 + u^7
    = 1 + 7(x^2(1+x)) + 21(x^2(1+x))2 + 35(x^2(1+x))^3 + 35(x^2(1+x))^4 ... + (x^2(1+x))^7

    to carry on seems like a rather unreasonable question, but I will assume you only want the term containing x^8

    if so, then x^8 can only arise in the expansions of
    35(x^2(1+x))^3 and 35(x^2(1+x))^4

    35(x^2(1+x))^3
    = 35x^6( 1 + 3x + 3x^2 + x^3)
    and the x^8 term from that is 105x^8

    35(x^2(1+x))^4
    = 35x^8( 1 + 4x + ... + x^4)
    and the only term with x^8 from that is 35x^8

    so the term containing x^8 is 105x^8+35x^8 = 140x^8

    check my arithmetic

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    arramge terms in each polynomial in ascending powers of y. y^3+xy^2+y+2-2x^2t+3xy^3+x^3 please help.
  2. binomial expansion

    how do you expand the following as a series of ascending powers of x upto x^2 using binomial expansion for this function (1+x)^2(1-5x)^14
  3. maths

    Use binomial theorem to to expand squareroot of 4+x in ascending powers of x to four terms.Give the limits for which the expansion is valid
  4. math

    Express (5x+2)/(2x-1)(x+1) into partial fractions and hence expand the expression as a series in ascending power of x giving the first 4 terms
  5. maths

    Obtain the binomial expansion of (2-x) (1+1/2x)^8 in ascending powers of x as far as the term in x^3. Use your result to estimate the value of 1.9 times (1.05)^8.
  6. maths

    Expand (1+2x)^20 - (1-2x)^20) in ascending powers of x up to the term in x^5 and use this result to evaluate (1.02)^20 - (0.98)^20 to 3 significant figures.
  7. maths

    Expand (1-6x)^4 (1+2x)^7 in ascending powers of x up to and includeing the terms in x^3.
  8. Math

    The sum of third and seventh term of an ascending arithmetic progression is 12 and their product is 32. Then find the ninth term?
  9. math

    Find the value of x for which thr middle term in the expansion of ( 1 + x ) ^ 20 in ascending powers of x is the geometric mean of the 9th and the 12th terms.
  10. Math

    Find the fifth term in the expansion of (4-1/5x)^9 in ascending powers of x

More Similar Questions