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Find binomial expansion of (1+x-x^2)^7 up to the term in x^3 watch

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    Hi, I've attempted this expansion by letting x-x^2 equal y, and so i did the expansion of (1+y)^7 and then substituted x-x^2 into the y values. However i got -42x^3, a coefficient of -42 for my x^3 term, but when i checked the solution using wolfram alpha, the coefficient should be 7.
    Have i done anything wrong? I don't understand what I've done wrong or how to get 7 instead of -42.
    Thanks
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    (Original post by soph99jk)
    Hi, I've attempted this expansion by letting x-x^2 equal y, and so i did the expansion of (1+y)^7 and then substituted x-x^2 into the y values. However i got -42x^3, a coefficient of -42 for my x^3 term, but when i checked the solution using wolfram alpha, the coefficient should be 7.
    Have i done anything wrong? I don't understand what I've done wrong or how to get 7 instead of -42.
    Thanks
    Well Wolfram says -7, not 7.

    You probably missed the x^3 term coming from the y^3 term, but just a guess, since you haven't posted any working.
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    (Original post by ghostwalker)
    Well Wolfram says -7, not 7.

    You probably missed the x^3 term coming from the y^3 term, but just a guess, since you haven't posted any working.
    Is there a quicker way to do questions like these?

    The other day, I had a question which was

    What is the coefficient of the x^3*y^5 term for the following function:

    (1+xy+y^2) ^n ?

    Anyway is it worth trying to learn the trinomial expansion? I had a quick look at it but it didn't make total sense.
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    (Original post by DrSebWilkes)
    Is there a quicker way to do questions like these?
    Usually they'll have made it so there's a way to limit the calculations, but you'll need to spot it - there's not a general easy approach.

    The other day, I had a question which was

    What is the coefficient of the x^3*y^5 term for the following function:

    (1+xy+y^2) ^n ?
    Here I'd bracket it as ((1+y^2)+xy)^n; it's immediate you only need to consider one term in this expansion (since it's the only possible way of getting an x^3 factor), and you then need to find the coefficient of the appropriate power of y in (1+y^2)^k (value of k should be obvious but I won't spell it out for you).

    Anyway is it worth trying to learn the trinomial expansion? I had a quick look at it but it didn't make total sense.
    It's much more usual (and barely more work) to expand (a+b+c)^n by bracketing 2 terms and expanding nominally (twice). So there's really no need to learn it.
 
 
 
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