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Long binomial expansion

mark

Write out

(4x-y)^{100}

using summation notation.

ksimmon1

(4x-y)^{100} = {\sum_{k=0}^{100}} \: {n\choose{k}}x^{100-k}y^{k}

mark

@ksimmon1 Not quite. Let’s change symbols to a and b to avoid confusion. Thus,

(a+b)^{100} = {\sum_{k=0}^{100}} \: {n\choose{k}}a^{100-k}b^{k}

Now, you have a= 4x and b=-y.