Phân tích các đa thức thành nhân tử

To simplify each expression:

1) X^2y + 2xy^2 - x - 2y:
This expression cannot be simplified further.

2) (X+2y)^3 - (x-2y)^3:
Using the formula for the difference of cubes, we have:
(X+2y)^3 - (x-2y)^3 = [(X+2y) - (x-2y)][(X+2y)^2 + (X+2y)(x-2y) + (x-2y)^2]
= (X+2y - x + 2y)[(X+2y)^2 + (X+2y)(x-2y) + (x-2y)^2]
= (2X + 4y - x)[X^2 + 4Xy + 4y^2 + X(x-2y) + 2y(x-2y) + (x-2y)^2]
= (2X + 4y - x)[X^2 + 4Xy + 4y^2 + X^2 - 2Xy + 2Xy - 4y^2 + 4xy - 4xy + 4y^2]
= (2X + 4y - x)[2X^2 + 4Xy + 4xy]
= 2(2X + 4y - x)(X^2 + 2Xy + 2xy)

3) (2x-1)(4x^2+2x+1):
Using the distributive property, we have:
(2x-1)(4x^2+2x+1) = 8x^3 + 4x^2 + 2x - 4x^2 - 2x - 1
= 8x^3 - 1

4) -y^2 + 2xy - x^2 + 25:
This expression cannot be simplified further.

5) X^2 - 2y + 2x - xy:
This expression cannot be simplified further.

6) 4x^2 - 16y^2:
Using the distributive property, we have:
4x^2 - 16y^2 = 4(x^2 - 4y^2)
= 4(x + 2y)(x - 2y)