a: =(a^2+2ab+b^2)+2(a+b)+1
=(a+b)^2+2(a+b)+1
=(a+b+1)^2
c: =3x(x-2y)-6y(x-2y)
=(x-2y)*3*(x-2y)
=3(x-2y)^2
g: =(x^3+8)-4x^2-8x
=(x+2)(x^2-2x+4)-4x(x+2)
=(x+2)(x^2-2x+4-4x)
=(x+2)(x^2-6x+4)
b: \(=ax^2+bx^2-ax-bx+a+b\)
=x^2(a+b)-x(a+b)+(a+b)
=(a+b)(x^2-x+1)
d: =(x-y)^2-(m-n)^2
=(x-y-m+n)(x-y+m-n)
f: =(2ab)^2-(a^2+b^2-1)^2
=(2ab-a^2-b^2+1)(2ab+a^2+b^2-1)
=[1-(a-b)^2][(a+b)^2-1]
=(a+b+1)(a+b-1)(1-a+b)(1+a-b)