Factorization(teach me plx)

1.
(x+y)^3 - 8(x-y)^3
=[(x+y)-2(x-y)][(x+y)^2+(x+y)(2)(x-y)+(2(x-y))^2]
=(x+y-2x+2y)(x^2+2xy+y^2+2(x^2-y^2)+4(x^2-2xy+y^2))
=(3y-x)(7x^2-6xy+3y^2)
2.
x^3-8
=x^3-2^3
=(x-2)(x^2+2x+2^2)
=(x-2)(x^2+2x+4)
x^3+2x-12
=x^3-8+2x-4
=(x-2)(x^2+2x+4)+2(x-2)
=(x-2)(x^2+2x+6)
3.
a^2 +2ab+2a+(b+1)^2
=a^2+2ab+2a+b^2+2b+1
=(a^2+2ab+b^2)+(2a+2b+1)
=(a+b)^2+2(a+b)+1
=(a+b+1)^2