因式分解 ............

解：
1、a^2-2a(b+c)+(b+c)^2
=[a-(b+c)]^2
=(a-b-c)^2

2、4x^2-4x(y-1)+(y-1)^2
=[2x-(y-1)]^2
=(2x-y+1)^2

3、-a+2a^2-a^3
=-a(1-2a+a^2)
=-a(1-a)^2
=-a(a-1)^2

4、3ax^2-3ay^2
=3a(x^2-y^2)
=3a(x+y)(x-y)

5、16a^2b-16a^3-4ab^2
= -4a(-4ab+4a^2+b^2)
=-4a(2a-b)^2

6、a^4-1
=(a^2+1)(a^2-1)
=(a^2+1)(a+1)(a-1)

7、x^4-18x^2+81
=(x^2-9)^2
=[(x+3)(x-3)]^2
=(x+3)^2(x-3)^2

8、x^4y^4-8x^2y^2+16
=(x^2y^2-4)^2
=(xy+2)^2(xy-2)^2

1. a^2-2a(b+c)+(b+c)^2 =(a-b-c)^2
2. 4x^2-4x(y-1)+(y-1)^2 =(2x-y+1)^2
3. -a+2a^2-a^3 =-a(a-1)^2
4. 3ax^2-3ay^2 =3a(x+y)(x-y)
5. 16a^2b-16a^3-4ab^2 =4a(2a-b)^2
6. a^4-1 =(a^2+1)(a+1)(a-1)
7. x^4-18x^2+81 =(x+3)^2(x-3)^2
8 x^4y^4-8x^2y^2+16=(xy+2)^2(xy-2)^2