how do you factor the following questions?

Question

1)A^4-B^4
2) 12A^2+AB-B^2
3)X^2-3x+XY-3Y
4) X^4+X^2-2

It'd be great to have some explanation with the answers. thanks

Answer 1

1) First, this is a difference of squares, so factors as
(A^2 + B^2)(A^2 - B^2); but now the second factor is again a difference of squares, so the complete factorization is
(A^2 + B^2)(A + B)(A - B).

2) (4A - B)(3A + B).

3) x(x - 3) + y(x - 3) = (x + y)(x - 3).

4) First, this is (x^2 + 2)(x^2 - 1), but the second factor is a difference of squares, so = (x^2 + 2)(x + 1)(x - 1).

Answer 2

1) it is a difference of 2 squares.. so the factors wold be (A^2-B^2) and (A^2+B^2)

2) I think theres a typo here or maybe I just dont know how to factor it

3) This could be factored through grouping...
x^2-3x+xy-3y could be arranged and factored out like-terms such that a common factor is drawn
x(x+y)-3(x+y)
(x-3)(x+y)

4) Reverse FOIL method i think
(x^2+2)(x^2-1)


Some polynomials can't be factored... just as prime numbers cant be