(a) Let n, k € Z with 0 ≤ k ≤n. Write down the formula for the binomial coefficient (7) and use it to prove the property that generates each row of Pascal's triangle from the previous one, namely n+1 (1) + (x + 1) = (+¹) k+1 for all n, k in the appropriate range. = (b) Let F = F(X,Y) (X4 – 2Y)⁹. Use the Binomial Theorem to determine the coefficients with which the following terms appear in F: (i) X ³²Y; (ii) X³6Y; (iii) X³y7.

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A: Solution...

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