Question

Представить выражение n(n+1)(n+2)(n+3)+1 в виде произведения двух многочленов

Answer 1

n² + 1n*n²+2n*n²+3n=n⁶*6n 

Answer 2

n(n+3)=k = n^2+3n
(n+1)(n+2) = n^2+3n+2 = k+2
n(n+1)(n+2)(n+3)+1=k*(k+2)+1 = k^2+2k+1 = (k+1)^2=(n^2+3n+1)*(n^2+3n+1)