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

Expanding both terms:

(2x-y)(2x-y) - (x+3y)(x+3y)
(4x^2 - 4xy + y^2) - (x^2 + 6xy + 9y^2)

Now we distribute the negative sign in the second term:

4x^2 - 4xy + y^2 - x^2 - 6xy - 9y^2

Combining like terms:

4x^2 - x^2 - 4xy - 6xy + y^2 - 9y^2
3x^2 - 10xy - 8y^2

So, (2x-y)^2 - (x+3y)^2 simplifies to 3x^2 - 10xy - 8y^2.