½(a²-2b²)²-2(a²-2b²)b²+2b^4 怎么分解因式

½(a²-2b²)²-2(a²-2b²)b²+2b^4 怎么分解因式
½(a²-2b²)²-2(a²-2b²)b²+2b^4 怎么分解因式

½(a²-2b²)²-2(a²-2b²)b²+2b^4 怎么分解因式
½(a²-2b²)²-2(a²-2b²)b²+2b^4
=½【(a²-2b²)²-4(a²-2b²)b²+4b^4】
=½（a²-2b²-2b²）²
=½（a²-4b²）²
=½（a-2b）²（a＋2b）²

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

½(a²-2b²)²-2(a²-2b²)b²+2b^4
=1/2[(a²-2b²)²-4(a²-2b²)b²+4b^4 ]
=1/2(a^2-2b^2-2b^2)^2
=1/2(a^2-4b^2)^2
=1/2(a+2b)^2(a-2b)^2