Prove the relation two ways: (a) State the polynomial expansion of (x + y)n as a summation of coefficients and powers of x and y. Then, make a simple substitution for x and y. (b) Prove the relation...

Prove the relation

two ways:

(a) State the polynomial expansion of (x + y)n as a summation of coefficients and powers of x and y. Then, make a simple substitution for x and y.

(b) Prove the relation by induction. Let

First confirm that the relation is valid for n = 1, i.e., that K (1) = 2¹. Now prove that
2K(n) for arbitrary