Find the coefficient of (x plus y)20?

Answer 1

The coefficient of ((x + y)^{20}) can be found using the binomial theorem, which states that ((a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k). In this case, the coefficient of each term in the expansion is given by (\binom{20}{k}), where (k) is the exponent of (y) and (n-k) is the exponent of (x). The specific coefficient for any term ((x^a y^b)) can be determined by choosing (a) and (b) such that (a + b = 20). For the overall expansion, the sum of the coefficients for all terms is (2^{20}).