因式分解:a³+2a²b-ab²-2b³=

因式分解:a³+2a²b-ab²-2b³=
因式分解:a³+2a²b-ab²-2b³=

因式分解:a³+2a²b-ab²-2b³=
a³+2a²b-ab²-2b³
=（a³+2a²b）-（ab²+2b³）
=a²（a+2b）-b²（a+2b）
=（a+2b）（a²-b²）
=（a+2b）（a+b）（a-b）

a³+2a²b-ab²-2b³
=a³-ab² +2a²b -2b³
=a(a²-b²) + 2b(a²-b²)
=(a+2b) (a²-b²)
= (a+2b) (a+b)(a-b)

a³+2a²b-ab²-2b³
=a²(a+2b)-b²(a+2b)
=(a+2b)(a²-b²)
=(a+2b)(a+b)(a-b)

f(a,b) = a³+2a²b-ab²-2b³
f(a,a) =0 => (a-b) is factor
f(a, -a) = 0 =>(a+b) is factor
f(a,b) = a³+2a²b-ab²-2b³
= (a-b)(a+b)(a+2b)