k(k+2)(2k+5)+3 如何变成 (k+1)(k+3)(2k+1)

问题描述:

k(k+2)(2k+5)+3 如何变成 (k+1)(k+3)(2k+1)

k(k+2)(2k+5)+3
=k(2k^2+9k+10)+3
=2k^3+9k^2+10k+3
=2k^3+2k^2+7k^2+10k+3
=2k^2(k+1)+(k+1)(7k+3)
=(k+1)(2k^2+7k+3)
=(k+1)(k+3)(2k+1)