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4 March, 10:56

If we wish to expand (x + y) 8, what is the coefficient of x 5 y 3? what is the coefficient of x 3 y 5?

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  1. 4 March, 13:57
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    We use the binomial theorem to answer this question. Suppose we have a trinomial (a + b) ⁿ, we can determine any term to be:

    [n! / (n-r) ! r!] a^ (r) b^ (n-r)

    a.) For x⁵y³, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.

    r = 5

    n - r = 3

    Solving for n,

    n = 3 + 5 = 8

    Therefore, the coefficient is equal to:

    Coefficient = n! / (n-r) ! r! = 8! / (8-5) !8! = 56

    b.) For x³y⁵, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.

    r = 3

    n - r = 5

    Solving for n,

    n = 5 + 3 = 8

    Therefore, the coefficient is equal to:

    Coefficient = n! / (n-r) ! r! = 8! / (8-3) !8! = 56
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