(a+b）^2-16a^2=a^2+2ab+b^2-16a^2=b^2+2ab-15a^2=(b+5a)(b-3a)
(x^2+4)^2-4x^2=(x^2+4)^2-(2x)^2=(x^2+2x+4)(x^2-2x+4)
m^4-2m^2n^2+n^4=(m^2-n^2)^2=(m+n)^2(m-n)^2
第4题是不是打错了,后一个括号里应该是减号吧：
(x^2-x)^2+1/2（x^2-x)+1/16=(x^2-x+1/4)^2=(x-1/2)^4
4m^2-n^2-6n-9=(2m)^2-(n^2+6n+9)=(2m)^2-(n+3)^2=(2m+n+3)(2m-n-3)
2a-4b+a^2-4b^2=(a^2+2a)-(4b^2+4b)=(a^2+2a+1)-(4b^2+4b+1)
=(a+1)^2-(2b+1)^2=(a+1+2b+1)(a+1-2b-1)=(a+2b+2)(a-2b)
(3a+b)^2-12ab=9a^2+6ab+b^2-12ab=9a^2-6ab+b^2=(3a-b)^2
(m-1)(m-3)+1=m^2-4m+3+1=m^2-4m+4=(m-2)^2
x^2(x^2-2)+1=x^4-2x^2+1=(x^2-1)^2=(x+1)^2(x-1)^2
-x^2-12xy-20y^2=-(x^2+12xy+20y^2)=-(x+2y)(x+10y)
3x^2-11xy+10y^2=(x-2y)(3x-5y)
第12题好象也打错了,第一个括号应该有个2次方的吧：
2(a-1)^2-11(a-1)+12=(a-1-4)[2(a-1)-3]=(a-5)(2a-5)
9a^4-7a^2+1=(9a^4-6a^2+1)-a^2=(3a^2-1)^2-a^2=(3a^2+a-1)(3a^2-a-1)
a^4+a^2b^2+b^4=(a^4+2a^2b^2+b^4)-a^2b^2=(a^2+b^2)^2-(ab)^2
=(a+ab+b)(a-ab+b)