分解因式a^5-1/2a^3b^2+1/16ab^4

来源:学生作业帮助网 编辑:六六作业网 时间:2025/01/30 17:07:45
分解因式a^5-1/2a^3b^2+1/16ab^4分解因式a^5-1/2a^3b^2+1/16ab^4分解因式a^5-1/2a^3b^2+1/16ab^4a^5-1/2a^3b^2+1/16ab^4

分解因式a^5-1/2a^3b^2+1/16ab^4
分解因式a^5-1/2a^3b^2+1/16ab^4

分解因式a^5-1/2a^3b^2+1/16ab^4
a^5-1/2a^3b^2+1/16ab^4
解原式=a(a^4-1/2a^2b^2+1/16b^4)
=a(a²-1/4b²)²
=a(a-1/2b)(a+1/2b)
楼上的1/16应该不能提出来

a^5-1/2a^3b^2+1/16ab^4
=a/16(16a^4-8a²b²+b^4)
=a/16(4a²-b²)²
=a/16(2a+b)²(2a-b)²