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Math Help - Find the coeficient

  1. #1
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    Find the coeficient

    Find the coefficient of the terms in x as indicated , in the following expansions .

    (a) (1+x)^2(2-3x)^7 , term in x^3

    (b) (x+\frac{1}{x})^2(1-x)^5 , term in x^2 .


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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    In the expansion of (a+b)^n the (n+1)th term is given by

     <br />
T_{n+1} = ~~ ^{n}C_r a^{n-r} b^{r}<br />


    (a)

    , term in x^3

    =(x^2+2x+1) (2-3x)^7

     <br />
=\underbrace{x^2(2-3x)^7}_a +\underbrace{2x(2-3x)^7}_b +\underbrace{ 1(2-3x)^7}_c<br />

    For (a)
    For getting x^3 the degree of x in second term should be one
    (see the formula above)
    Hence
    in
    (2-3x)^7



     <br />
T_2 = ~~^7 C_1 2^{7-1} (-3x)^{1}<br />

    eliminate x to get value of coefficient
    Go ahead with the b and c other terms

    2)

    (b) , term in x^2 .

    If you understood 1 you can do it tell incase if you get stuck again
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