x^2+xy =x(x+y)
ax^2-4ax+4a =a(x^2-4x+4)=a(x-2)^2
x^4-16y^4=(x^2+4y^2)(x^2-4y^2)=(x^2+4y^2)(x+2y)(x-2y)
(x-1)^2-9=(x-1+3)(x-1-3)=(x+2)(x-4)
(2a-b)^2+8ab =4a^2-4ab+b^2+8ab=4a^2+4ab+b^2=(2a+b)^2
9(a-b)^2-25(a+b)^2=(3a-3b+5a+5b)(3a-3b-5a-5b)=(8a+2b)(-2a-8b)