(x²+2x)²+2（x²+2x）+1因式分解,

(x²+2x)²+2（x²+2x）+1因式分解,
(x²+2x)²+2（x²+2x）+1因式分解,

(x²+2x)²+2（x²+2x）+1因式分解,
(x²+2x)²+2（x²+2x）+1
设x²+2x=t
则t²+2t+1=（t+1）²
=（x²+2x+1）²
=（x+1）^4

(x²+2x)²+2（x²+2x）+1
=（x²+2x+1)²

(x^2+2x)2+2(x^2+2x)+1
=[(x^2+2x)+1]^2
=(x^2+2x+1)^2
=[(x+1)^2]^2
=(x+1)^4

设x²+2x=t
则原式=t²+2t+1=(t+1)²
将t代入
原式=（x²+2x+1）²=（x+1)^4