Simplify the following:
3 x^2-y^2-(4 x^2-y^2)
4 x^2-y^2 = (2 x)^2-y^2:
3 x^2-y^2-((2 x)^2-y^2)
Factor the difference of two squares. (2 x)^2-y^2 = (2 x-y) (2 x+y):
3 x^2-y^2-(2 x-y) (2 x+y)
(2 x+y) (2 x-y) = (2 x) (2 x) + (2 x) (-y) + (y) (2 x) + (y) (-y) = 4 x^2-2 x y+2 x y-y^2 = 4 x^2-y^2:
3 x^2-y^2-4 x^2-y^2
-(4 x^2-y^2) = y^2-4 x^2:
3 x^2-y^2+y^2-4 x^2
Grouping like terms, 3 x^2-y^2-4 x^2+y^2 = (y^2-y^2)+(3 x^2-4 x^2):
(y^2-y^2)+(3 x^2-4 x^2)
3 x^2-4 x^2 = -x^2:
-x^2+(y^2-y^2)
y^2-y^2 = 0:
Answer: |-x^2
