(A^2+2A)(A^2+2A+2)+1

(A^2+2A)(A^2+2A+2)+1

=（a²+2a）²+2(a²+1)+1

=(a²+2a+1)²

=(a+1)^4

将a²+2a看作一个整体

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(a²+2a)(a²+2a+2)+1
=(a²+2a)²+2(a²+2a)+1
=[(a²+2a)+1]²
=[(a+1)²]²
=(a+1)的4次方

设A^2+2A=B
则B（B+2）+1
=B^2+2B+1
=(B+1)^2
=(A^2+2A+1)^2
=(A+1)^4