a³-8-6a²+12a因式分解

a³-8-6a²+12a因式分解
a³-8-6a²+12a因式分解

a³-8-6a²+12a因式分解
a³-8-6a²+12a
=a³-2³-6a(a-2)
=(a-2)(a²+2a+4)-6a(a-2)
=(a-2)(a²-4a+4)
=(a-2)(a-2)²
=(a-2)³

(a-2)(a^2+2a+4)-6a(a-2)=(a-2)(a^2-4a+4)=(a-2)^3

原式=（a－2）的立方

a³-8-6a²+12a
=a³-2a²-4a²+8a+4a-8
=a²（a-2）-4a（a-2）+4（a-2）
=（a²-4a+4）（a-2）
=（a-2）³

(a-2)(a的平方-4a+4)

a³-8-6a²+12a
(a³-8)-(6a²-12a)
=(a³-2³)-6a(a-2)
=[(a-2)(a²+2a+4)]-6a(a-2)
=(a-2)(a²-4a+4)
=(a-2)(a-2)²
=(a-2)³