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Expression simplification/ Factor perfect squares/ -x^2+4*x*y-y^2

Factor -x^2+4*x*y-y^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2            2
- x  + 4*x*y - y
$$- y^{2} + \left(- x^{2} + 4 x y\right)$$ 
-x^2 + (4*x)*y - y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- y^{2} + \left(- x^{2} + 4 x y\right)$$
Let us write down the identical expression
$$- y^{2} + \left(- x^{2} + 4 x y\right) = 3 y^{2} + \left(- x^{2} + 4 x y - 4 y^{2}\right)$$
or
$$- y^{2} + \left(- x^{2} + 4 x y\right) = 3 y^{2} - \left(x - 2 y\right)^{2}$$
General simplification [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Factorization [src] 
/      /      ___\\ /      /      ___\\
\x - y*\2 - \/ 3 //*\x - y*\2 + \/ 3 //
$$\left(x - y \left(2 - \sqrt{3}\right)\right) \left(x - y \left(\sqrt{3} + 2\right)\right)$$ 
(x - y*(2 - sqrt(3)))*(x - y*(2 + sqrt(3)))
Numerical answer [src] 
-x^2 - y^2 + 4.0*x*y
-x^2 - y^2 + 4.0*x*y
Rational denominator [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Combining rational expressions [src] 
   2               
- y  + x*(-x + 4*y)
$$x \left(- x + 4 y\right) - y^{2}$$ 
-y^2 + x*(-x + 4*y)
Assemble expression [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Trigonometric part [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Combinatorics [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Common denominator [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
Powers [src] 
   2    2        
- x  - y  + 4*x*y
$$- x^{2} + 4 x y - y^{2}$$ 
-x^2 - y^2 + 4*x*y
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