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

Factor y^2+y*a+2*a^2 squared

An expression to simplify:

The solution

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