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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
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
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
$$5 x^{2} + \left(- x 4 y - y^{2}\right) = - \frac{9 y^{2}}{5} + \left(5 x^{2} - 4 x y + \frac{4 y^{2}}{5}\right)$$
or
$$5 x^{2} + \left(- x 4 y - y^{2}\right) = - \frac{9 y^{2}}{5} + \left(\sqrt{5} x - \frac{2 \sqrt{5} y}{5}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{9}{5}} y + \left(\sqrt{5} x + - \frac{2 \sqrt{5}}{5} y\right)\right) \left(\sqrt{\frac{9}{5}} y + \left(\sqrt{5} x + - \frac{2 \sqrt{5}}{5} y\right)\right)$$
$$\left(- \frac{3 \sqrt{5}}{5} y + \left(\sqrt{5} x + - \frac{2 \sqrt{5}}{5} y\right)\right) \left(\frac{3 \sqrt{5}}{5} y + \left(\sqrt{5} x + - \frac{2 \sqrt{5}}{5} y\right)\right)$$
$$\left(\sqrt{5} x + y \left(- \frac{3 \sqrt{5}}{5} - \frac{2 \sqrt{5}}{5}\right)\right) \left(\sqrt{5} x + y \left(- \frac{2 \sqrt{5}}{5} + \frac{3 \sqrt{5}}{5}\right)\right)$$
$$\left(\sqrt{5} x - \sqrt{5} y\right) \left(\sqrt{5} x + \frac{\sqrt{5} y}{5}\right)$$
Factorization [src] 
/    y\        
|x + -|*(x - y)
\    5/
$$\left(x - y\right) \left(x + \frac{y}{5}\right)$$ 
(x + y/5)*(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
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
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
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
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
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)
Combinatorics [src] 
(x - y)*(y + 5*x)
$$\left(x - y\right) \left(5 x + y\right)$$ 
(x - y)*(y + 5*x)
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