Question

Determine a soma dos coeficientes numéricos no desenvolvimentos dos binôminos
(3x + 2y)⁵

Answer 1

Boa tarde Rodrigo

binômio de Newton

C(n,k) = n!/(n-k)k!

C(5,0) = 1
C(5,1) = 5
C/5,2) = 10
C(5,3) = 10
C(5,4) = 5
C(5,5) = 1

S = 1*3^5*2^0 + 5*3^4*2^1 + 10*3^3*2^2 + 10*3^2*2^3 + 5*3^1*2^4 + 1*3^0*2^5

S = 243 + 810 + 1080 + 720 + 240 + 32 = 3125