Posted by Ethan on Sunday, October 2, 2011 at 9:04am.
Expand [1+x^2(1+x)]^7 in ascending powers of x as the term in x^8.

Math  Damon, Sunday, October 2, 2011 at 10:33am
Use binomial expansion over and over again

Math  Reiny, Sunday, October 2, 2011 at 10:40am
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
Answer This Question
Related Questions
 maths  Expand (1+2x)^20  (12x)^20) in ascending powers of x up to the term in...
 maths  Expand (16x)^4 (1+2x)^7 in ascending powers of x up to and includeing ...
 Math  Find the fifth term in the expansion of (41/5x)^9 in ascending powers of...
 maths  Use binomial theorem to to expand squareroot of 4+x in ascending powers ...
 math  Find the value of x for which thr middle term in the expansion of ( 1 + x...
 maths  Obtain the binomial expansion of (2x) (1+1/2x)^8 in ascending powers of...
 binomial expansion  how do you expand the following as a series of ascending ...
 Math  The sum of third and seventh term of an ascending arithmetic progression ...
 Math  arramge terms in each polynomial in ascending powers of y. y^3+xy^2+y+2...
 math  Express (5x+2)/(2x1)(x+1) into partial fractions and hence expand the ...
More Related Questions