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Core 2 - Binomial Expansion

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    a) Find the coefficent of x in the expansion (2+x)^9

    b)find the coefficent of x in the expansion (1-2x)^4(2+x)^9

    not sure on how to do these questions could someone help please.
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    Can you use the binomial expansion?
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    Errr i guess so
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    (Original post by Gary)
    Errr i guess so
    First expand (2+x)^9 binomially, then look at the number infront of the x term= co-efficient of the x term.

    Expand (1-2x)^4 binomially and multiply between the brackets only to get 'x' terms. Then you should be able to identify the co-efficient of x.
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    (Original post by Gary)
    Errr i guess so
    I think the other other poster meant can YOU use the Binomial Expansion ....

    If the answer is yes then I am not sure why you are asking for help??
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    (Original post by Gary)
    a) Find the coefficent of x in the expansion (2+x)^9

    b)find the coefficent of x in the expansion (1-2x)^4(2+x)^9

    not sure on how to do these questions could someone help please.
    there isn't much point in expanding the whole thing out.. just think about the terms that you need...
    i.e.

    (9C1) * (2^8) * (x) + (4C1) * (-2x) * (2^9)
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    (Original post by Gary)
    a) Find the coefficent of x in the expansion (2+x)^9

    b)find the coefficent of x in the expansion (1-2x)^4(2+x)^9

    not sure on how to do these questions could someone help please.
    For a)

    There is 1 term in binomial expansion with x.
    \displaystyle \left (2+x\right )^9=\binom{9}{0}2^9\cdot x^0 +\binom {9}{1}2^8x^1+ ...

    For b)
    Expanding it and multiplying out íou get x with coefficients in two case
    1. In expansion of (1-2x)^4 x is on 0 power and in expansion of (2+x)^9 x is on 1 power
    \displaystyle \binom{4}{0}\cdot 1^9 \cdot \binom{9}{1}2^8 \cdot x

    2. In exoansion of (1-2x)^4 x is on 1 power and in expansion of (2+x)^9 x is on 0 power
    \displaystyle \binom{4}{1}\cdot (-2)x \cdot \binom {9}{0}2^9

    Calculate these term and add them together and you will get the coefficient.
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    hmmm im not sure how to do it without expanding the whole thing out, cause im pretty sure theres a method where you dont have to expand the whole thing
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    (Original post by Gary)
    hmmm im not sure how to do it without expanding the whole thing out, cause im pretty sure theres a method where you dont have to expand the whole thing
    I think you have been given plenty of clues, but If you can't see what to do, why don't you START the expansion?

    The x term is near the beginning - so you won't have to expand the whole thing.

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