分解因式:a的4次方+a的的立方2a的平方+a+1
问题描述：
分解因式:a的4次方+a的的立方2a的平方+a+1
答
分解因式:
a的4次方+a³-2a²+a+1
=a²(a²+a-2)+(a+1)
=a²(a+1)(a-2)+(a+1)
=(a+1)[a²(a-2)+1]
=(a+1)(a³-2a²+1)
=(a+1)[a²(a-1)-(a²-1)]
=(a+1)[a²(a-1)-(a+1)(a-1)]
=(a+1)(a-1)(a²-a-1)