Question

把(t^2+2t)^2+2(t^2+2t)+1分解因式,并求当t=13时的值

这道题应该怎么解答?

Answer 1

（t^2+2t)^2+2(t^2+2t)+1 (把t^2+2t看做整体)
=（t^2+2t+1）^2
=(t+1)^4
当t=13时原式=（13+1）^4= 65 536

追问

搞错了,t=-3

追答

t=-3时原式=16
= =！我也打错了。。14打成16了

Answer 2

(t^2+2t)^2+2(t^2+2t)+1
=(t²+2t+1)²
=(t+1)^4 当t=13时
=(13+1)^4
=14^4
=38416

Answer 3

令a=t²+2t

a²+2a+1
=(a+1)²
=(t²+2t+1)²
=[(t+1)²]²
=196x196
=38416