a的四次方+2a的3次方+3a的平方+2a+1

题目

a的四次方+2a的3次方+3a的平方+2a+1

答案

a^4+2a^3+3a^2+2a+1
=a^2[a^2+1/a^2+2(a+1/a)+3]
=a^2[(a+1/a)^2+2(a+1/a)+1]
=a^2(a+1/a+1)^2
=(a^2+a+1)^2