Monday

October 20, 2014

October 20, 2014

Posted by **Ethan** on Sunday, October 2, 2011 at 9:04am.

- Math -
**Damon**, Sunday, October 2, 2011 at 10:33amUse binomial expansion over and over again

- Math -
**Reiny**, Sunday, October 2, 2011 at 10:40amlet 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 - (1-2x)^20) in ascending powers of x up to the term in...

maths - Expand (1-6x)^4 (1+2x)^7 in ascending powers of x up to and includeing ...

maths - Use binomial theorem to to expand squareroot of 4+x in ascending powers ...

maths - Obtain the binomial expansion of (2-x) (1+1/2x)^8 in ascending powers of...

binomial expansion - how do you expand the following as a series of ascending ...

Math - arramge terms in each polynomial in ascending powers of y. y^3+xy^2+y+2-...

math - Express (5x+2)/(2x-1)(x+1) into partial fractions and hence expand the ...

Algebra 1 - Arrange the terms of -3x+4x^5 - 2x^3 so that the powers of x are in ...

Precalc - 1) expand (1+3x)^4 using the Binomial Theorem. 2) Use Pascal's ...

math - Write 2005693 in expand form using powers of tens