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Expression simplification/ Factor perfect squares/ y^2-y*x+10*x^2

Factor y^2-y*x+10*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2             2
y  - y*x + 10*x
$$10 x^{2} + \left(- x y + y^{2}\right)$$ 
y^2 - y*x + 10*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$10 x^{2} + \left(- x y + y^{2}\right)$$
Let us write down the identical expression
$$10 x^{2} + \left(- x y + y^{2}\right) = \frac{39 y^{2}}{40} + \left(10 x^{2} - x y + \frac{y^{2}}{40}\right)$$
or
$$10 x^{2} + \left(- x y + y^{2}\right) = \frac{39 y^{2}}{40} + \left(\sqrt{10} x - \frac{\sqrt{10} y}{20}\right)^{2}$$
General simplification [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Factorization [src] 
/      /        ____\\ /      /        ____\\
|    y*\1 - I*\/ 39 /| |    y*\1 + I*\/ 39 /|
|x - ----------------|*|x - ----------------|
\           20       / \           20       /
$$\left(x - \frac{y \left(1 - \sqrt{39} i\right)}{20}\right) \left(x - \frac{y \left(1 + \sqrt{39} i\right)}{20}\right)$$ 
(x - y*(1 - i*sqrt(39))/20)*(x - y*(1 + i*sqrt(39))/20)
Numerical answer [src] 
y^2 + 10.0*x^2 - x*y
y^2 + 10.0*x^2 - x*y
Rational denominator [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Assemble expression [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Common denominator [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Powers [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Combining rational expressions [src] 
    2            
10*x  + y*(y - x)
$$10 x^{2} + y \left(- x + y\right)$$ 
10*x^2 + y*(y - x)
Combinatorics [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
Trigonometric part [src] 
 2       2      
y  + 10*x  - x*y
$$10 x^{2} - x y + y^{2}$$ 
y^2 + 10*x^2 - x*y
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