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Expression simplification/ Factor perfect squares/ y^2-y*x+7*x^2

Factor y^2-y*x+7*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*x + 7*x
$$7 x^{2} + \left(- x y + y^{2}\right)$$ 
y^2 - y*x + 7*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$7 x^{2} + \left(- x y + y^{2}\right)$$
Let us write down the identical expression
$$7 x^{2} + \left(- x y + y^{2}\right) = \frac{27 y^{2}}{28} + \left(7 x^{2} - x y + \frac{y^{2}}{28}\right)$$
or
$$7 x^{2} + \left(- x y + y^{2}\right) = \frac{27 y^{2}}{28} + \left(\sqrt{7} x - \frac{\sqrt{7} y}{14}\right)^{2}$$
Factorization [src] 
/      /          ___\\ /      /          ___\\
|    y*\1 - 3*I*\/ 3 /| |    y*\1 + 3*I*\/ 3 /|
|x - -----------------|*|x - -----------------|
\            14       / \            14       /
$$\left(x - \frac{y \left(1 - 3 \sqrt{3} i\right)}{14}\right) \left(x - \frac{y \left(1 + 3 \sqrt{3} i\right)}{14}\right)$$ 
(x - y*(1 - 3*i*sqrt(3))/14)*(x - y*(1 + 3*i*sqrt(3))/14)
General simplification [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Numerical answer [src] 
y^2 + 7.0*x^2 - x*y
y^2 + 7.0*x^2 - x*y
Assemble expression [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Combinatorics [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Combining rational expressions [src] 
   2            
7*x  + y*(y - x)
$$7 x^{2} + y \left(- x + y\right)$$ 
7*x^2 + y*(y - x)
Common denominator [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Rational denominator [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Trigonometric part [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
Powers [src] 
 2      2      
y  + 7*x  - x*y
$$7 x^{2} - x y + y^{2}$$ 
y^2 + 7*x^2 - x*y
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