2(x-y)+2(2x-3y)

To simplify the expression 2(x-y) + 2(2x-3y), you'll distribute the 2 within the parentheses to each of the terms inside and then combine like terms.

First distribute:

2 * x = 2x 2 * (-y) = -2y

Then distribute for the second set of parentheses:

2 * 2x = 4x 2 * (-3y) = -6y

Now, add the distributed terms:

2x - 2y + 4x - 6y

Combine the like terms (2x and 4x) and (-2y and -6y):

2x + 4x = 6x -2y - 6y = -8y

Finally, the simplified expression is:

6x - 8y

That is the fully simplified form of 2(x-y) + 2(2x-3y).