作业帮(x-1/2)²(x²+1/4)²(x+1/2)²
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 07:04:44
(x-1/2)²(x²+1/4)²(x+1/2)²
(x-1/2)²(x²+1/4)²(x+1/2)²
(x-1/2)²(x²+1/4)²(x+1/2)²
原式=[(x-1/2)(x+1/2)(x²+1/4)]²
=[(x²-1/4)(x²+1/4)]²
=(x^4-1/4)²
=x^8-1/2x^4+1/16
答：
连续应用平方差公式
(x-1/2)²(x²+1/4)²(x+1/2)²
=[(x-1/2)(x²+1/4)(x+1/2)]²
=[(x-1/2)(x+1/2)(x²+1/4)]²
=[(x²-1/4)(x²+1/4)]²
=(x^4-1/16)²
=x^8-(x^4)/8+1/256