algebra 2

can someone tell me how to expand the bionomial (d-2)^6?

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  1. (d-2)^6
    is the same as (d-2)*(d-2)*.... six times.
    You can expand it by multiplication, or you can use the binomial expansion formula, where

    =a^n + na^(n-1)b + n(n-1)/2!a^(n-2)b^2 +
    + ...b^n

    where the general term i is
    n(n-1)(n-2)..(n-i)/i! * a^(n-i)b^i

    Expanding along these lines, we get for
    n=1, (a+b)^1 = a+b
    n=2, (a+b)^2 = a^2+2ab+b^2
    n=3, (a+b)^3 = a^3+3a^2b+3ab^2+b^3
    with the coefficients being
    1 1
    1 2 1
    1 3 3 1
    1 4 6 4 1
    1 5 10 10 5 1
    1 6 15 21 15 6 1
    Each coefficient is the sum of the one immediately above plus the one to the left.
    This pattern is called the pascal's triangle.

    For more reading, see:

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    posted by MathMate

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