用乘法公式分解因式

1.
1/2a^2-2ab+2b^2
=1/2(a^2-4ab+4b^2)
=1/2(a-2b)^2
2.
2x^3y+8x^2y^2+8xy^3
=2xy(x^2+4xy+4y^2)
=2xy(x+2y)^2
3.
-9x^2-3xy-1/4y^2
=-(3x+1/2y)^2
4.
(x^2-x)^2+6(x^2-x)+9
=(x^2-x+3)^2
5.
(x^2-2x)^2+2x(x-2)+1
=(x^2-2x+1)^2
=(x-1)^4
6.
9a^2-30ab^2+25b^4
=(3a-5b^2)^2
7.
-4x^2+12xy-9y^2
=-(2x-3y)^2
8.
9(2a-b)^2-6(2a-b)+1
=[3(2a-b)-1]^2
=(6a-3b-1)^2
9.
-2m^3+24m^2-72m
=-2m(m^2-12m+36)
=-2m(m-6)^2
10.
-x^4+2x^2y^2-y^4
=-(x^2-y^2)
=-(x+y)(x-y)
11.
(x+y)^2+4(x-y)^2-4(x^2-y^2)
=(x+y)^2-4(X+y)(X-y)+4(x-y)^2
=[(x+y)-2(x-y)]^2
=(3y-x)^2
12.
(a^2+1)^2-4a^2
=(a^2+1-2a)^2
=(a-1)^4