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Expression simplification/ Factor perfect squares/ -y^2-4*y*x-5*x^2

Factor -y^2-4*y*x-5*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2              2
- y  - 4*y*x - 5*x
$$- 5 x^{2} + \left(- x 4 y - y^{2}\right)$$ 
-y^2 - 4*y*x - 5*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 x^{2} + \left(- x 4 y - y^{2}\right)$$
Let us write down the identical expression
$$- 5 x^{2} + \left(- x 4 y - y^{2}\right) = - \frac{y^{2}}{5} + \left(- 5 x^{2} - 4 x y - \frac{4 y^{2}}{5}\right)$$
or
$$- 5 x^{2} + \left(- x 4 y - y^{2}\right) = - \frac{y^{2}}{5} - \left(\sqrt{5} x + \frac{2 \sqrt{5} y}{5}\right)^{2}$$
Factorization [src] 
/    y*(-2 + I)\ /    y*(2 + I)\
|x - ----------|*|x + ---------|
\        5     / \        5    /
$$\left(x - \frac{y \left(-2 + i\right)}{5}\right) \left(x + \frac{y \left(2 + i\right)}{5}\right)$$ 
(x - y*(-2 + i)/5)*(x + y*(2 + i)/5)
General simplification [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Numerical answer [src] 
-y^2 - 5.0*x^2 - 4.0*x*y
-y^2 - 5.0*x^2 - 4.0*x*y
Trigonometric part [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Combinatorics [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Combining rational expressions [src] 
     2               
- 5*x  + y*(-y - 4*x)
$$- 5 x^{2} + y \left(- 4 x - y\right)$$ 
-5*x^2 + y*(-y - 4*x)
Common denominator [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Powers [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Assemble expression [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
Rational denominator [src] 
   2      2        
- y  - 5*x  - 4*x*y
$$- 5 x^{2} - 4 x y - y^{2}$$ 
-y^2 - 5*x^2 - 4*x*y
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