(x + 1) (x + 2) (x + 3); (x + 19) (x + 20) expansion of the coefficient of the 18th power of X! Super

(x + 1) (x + 2) (x + 3); (x + 19) (x + 20) expansion of the coefficient of the 18th power of X! Super

A total of 20 factors, 18 times, there are two are multiplied by the constant, Biro, the first 18 are the product of X, the final coefficient is 19 * 20, careful analysis, not particularly difficult, the answer may be: the number of 20, the sum of any two products: 1 * 2 + 1 * 3 + 1 * 4 +... + 1 * 20 + 2 * 3 + 2 * 4 + 2 * 5 +. + 2 * 20 + 3 * 4 + 3 * 5 + 3 *

If the sum of the coefficients in the n-th power expansion of the polynomial (3x + 1 / x) is 256, then the coefficients of the 4-th power of X in the n-th power expansion of (x + X + 1) multiplied by (x-1) are equal

Answer: 54
Let 4 ^ n of x = 1 = 256, so n = 4, so the coefficient of x ^ 2 is C_ (4 2)×3^2=54
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Find the coefficient of X term in (x ^ 2-3x-1) ^ 10 expansion

Nine (- 1) and one (- 3x) are multiplied by a combination of 10 (- 1) ^ 9 * (- 3x) = 30x