Question

(x-y)^2+(x+y)^2-2(x+y)(x-y)=4x^2

Answer 1

(х-у)²+(х+у)²-2(х+у)(х-у)=4х²

х²-2ху+у²+х²+2ху+у²-2х²+2у²-4х²=0

4у²-4х²=0

у²=х²

|у|=|х|

Answer 2

Let's simplify the given expression step by step:

(x - y)^2 + (x + y)^2 - 2(x + y)(x - y) = 4x^2

First, expand the squares:

(x^2 - 2xy + y^2) + (x^2 + 2xy + y^2) - 2(x^2 - y^2) = 4x^2

Now, combine like terms:

x^2 - 2xy + y^2 + x^2 + 2xy + y^2 - 2x^2 + 2y^2 = 4x^2

Combine like terms again:

(2x^2 + 2y^2) - 2x^2 + 2y^2 = 4x^2

Now, simplify the left side:

2x^2 + 2y^2 - 2x^2 + 2y^2 = 4x^2

The terms -2x^2 and +2x^2 cancel each other out, leaving:

2y^2 + 2y^2 = 4x^2

Now, combine like terms again:

4y^2 = 4x^2

Finally, divide both sides by 4 to isolate x^2:

y^2 = x^2

So, the simplified equation is:

y^2 = x^2