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Math Help - Find the coefficient a of the term in the expansion of this binomial

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    Find the coefficient a of the term in the expansion of this binomial

    Find the coefficient a of the term in the expansion of this binomial

    (x^2+y)^10 TERM: ax^8y^6
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    Quote Originally Posted by thepride View Post
    Find the coefficient a of the term in the expansion of this binomial

    (x^2+y)^10 TERM: ax^8y^6
    The general term is {10 \choose r} (x^{2})^r y^{10 - r} = {10 \choose r} x^{2r} y^{10 - r}. What value of r will give you the required term? Use that value to get the coefficient.
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    Quote Originally Posted by thepride View Post
    Find the coefficient a of the term in the expansion of this binomial

    (x^2+y)^10 TERM: ax^8y^6
    You can use Pascal's Triangle to perform Binomial Expansion. There are lots of very good explanations of how to do this on the web. Just run a search for "binomial expansion pascal triangle".

    Look at the 10th row of Pascal's Triangle. To make this problem look like a 'normal' one, you can let a=x^2 and b=y. Then you'll be looking for the term when a is to the 4th power and b is to the 6th power.

    The first number in the 10th row is the coefficient for a^{10}b^{0}. The second number is the coefficient for a^9b^1. And so on with the exponent on a decreasing and the exponent on b decreasing. You'll be looking for the 7th number in the 10th row.
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