Factoring polynomials using the distributive property

[onmyown]

HI, I am having trouble getting the correct answer for this problem:
4x^2+8y-4xy-8x

I have made several attempts. Here is one of them:
4x^2+8y-4xy-8x
1) Grouped like terms together:
= (4x^2 + (-8x))+(8y + (-4xy))
2) Factored each term:
(2*2*x*x + (-1)*2*2*2*x) + (2*2*2*y + (-1)*2*2*x*y)
3) Found greatest common factor for each pair of like terms, and factored each pair by its GCF:
(4x*x+4x*(-2)) + (4y*2+4y*-x)
4) Used distributive property:
4x(x-2) + 4y(2-x)
5) Therefore, the solution to the problem is the binomial:
(4x+4y)(x-2)

However, this is wrong. The actual answer is (4x-4y)(x-2). So, I'm correct, except for the fact that 4y is positive when it should be negative.
Can someone please help understand why 4y is actually -4y?

[stapel_eliz]

4) Used distributive property:
4x(x-2) + 4y(2-x)
5) Therefore, the solution to the problem is the binomial:
(4x+4y)(x-2)

How did the "2 - x" turn into "x - 2"? Is 5 - 3 the same value as 3 - 5?

[onmyown]

4) Used distributive property:
4x(x-2) + 4y(2-x)
5) Therefore, the solution to the problem is the binomial:
(4x+4y)(x-2)

How did the "2 - x" turn into "x - 2"? Is 5 - 3 the same value as 3 - 5?

I got the right answer now. Thanks