分类：教育/科学-理工学科-数学
问题：因式分解a（a
a（a-b)^3+2a^(a-b)^2-2ab(b-a)^2
9(2a-b)^2-25(a-2b)^2
1-m^4n^4
-4x^2-8xy-4y^2+8x+8y-4
x^4+4
xy+(x+1)(y+1)（xy+1)
回答：①
a(a-b)^3+2a^2(a-b)^2-2ab(b-a)^2
=a(a-b)^2[(a-b)+2a-2b]
=3a(a-b)^3.

②
9(2a-b)^2-25(a-2b)^2
=[3(2a-b)+5(a-2b)][3(2a-b)-5(a-b)]
=(11a-13b)(a+2b).

③
1-m^4n^4
=(1+m^2n^2)(1-m^2n^2)
=(1+m^2n^2)(1+mn)(1-mn).

④
-4x^2-8xy-4y^2+8x+8y-4
=-4(x^2+2xy+y^2)+8(x+y)-4
=-4(x+y)^2+8(x+y)-4
=-4[(x+y)^2-2(x+y)+1]
=-4(x+y-1)^2.

⑤
x^4+4
=(x^4+4x^2+4)-4x^2
=(x^2+2)^2-(2x)^2
=(x^2+2x+2)(x^2-2x+2).