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

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

An expression to simplify:

The solution

You have entered [src] 
   2          2
2*x  + x*y + y
$$y^{2} + \left(2 x^{2} + x y\right)$$ 
2*x^2 + x*y + y^2
General simplification [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$y^{2} + \left(2 x^{2} + x y\right)$$
Let us write down the identical expression
$$y^{2} + \left(2 x^{2} + x y\right) = \frac{7 y^{2}}{8} + \left(2 x^{2} + x y + \frac{y^{2}}{8}\right)$$
or
$$y^{2} + \left(2 x^{2} + x y\right) = \frac{7 y^{2}}{8} + \left(\sqrt{2} x + \frac{\sqrt{2} y}{4}\right)^{2}$$
Factorization [src] 
/      /         ___\\ /      /        ___\\
|    y*\-1 + I*\/ 7 /| |    y*\1 + I*\/ 7 /|
|x - ----------------|*|x + ---------------|
\           4        / \           4       /
$$\left(x - \frac{y \left(-1 + \sqrt{7} i\right)}{4}\right) \left(x + \frac{y \left(1 + \sqrt{7} i\right)}{4}\right)$$ 
(x - y*(-1 + i*sqrt(7))/4)*(x + y*(1 + i*sqrt(7))/4)
Numerical answer [src] 
y^2 + 2.0*x^2 + x*y
y^2 + 2.0*x^2 + x*y
Combining rational expressions [src] 
 2              
y  + x*(y + 2*x)
$$x \left(2 x + y\right) + y^{2}$$ 
y^2 + x*(y + 2*x)
Rational denominator [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
Common denominator [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
Assemble expression [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
Combinatorics [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
Powers [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
Trigonometric part [src] 
 2      2      
y  + 2*x  + x*y
$$2 x^{2} + x y + y^{2}$$ 
y^2 + 2*x^2 + x*y
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