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Expression simplification/ Factor perfect squares/ y^2+y*q+4*q^2

Factor y^2+y*q+4*q^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  + y*q + 4*q
$$4 q^{2} + \left(q y + y^{2}\right)$$ 
y^2 + y*q + 4*q^2
General simplification [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Factorization [src] 
/      /         ____\\ /      /        ____\\
|    y*\-1 + I*\/ 15 /| |    y*\1 + I*\/ 15 /|
|q - -----------------|*|q + ----------------|
\            8        / \           8        /
$$\left(q - \frac{y \left(-1 + \sqrt{15} i\right)}{8}\right) \left(q + \frac{y \left(1 + \sqrt{15} i\right)}{8}\right)$$ 
(q - y*(-1 + i*sqrt(15))/8)*(q + y*(1 + i*sqrt(15))/8)
The perfect square
Let's highlight the perfect square of the square three-member
$$4 q^{2} + \left(q y + y^{2}\right)$$
Let us write down the identical expression
$$4 q^{2} + \left(q y + y^{2}\right) = \frac{15 y^{2}}{16} + \left(4 q^{2} + q y + \frac{y^{2}}{16}\right)$$
or
$$4 q^{2} + \left(q y + y^{2}\right) = \frac{15 y^{2}}{16} + \left(2 q + \frac{y}{4}\right)^{2}$$
Numerical answer [src] 
y^2 + 4.0*q^2 + q*y
y^2 + 4.0*q^2 + q*y
Combinatorics [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Combining rational expressions [src] 
   2            
4*q  + y*(q + y)
$$4 q^{2} + y \left(q + y\right)$$ 
4*q^2 + y*(q + y)
Trigonometric part [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Common denominator [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Rational denominator [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Powers [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
Assemble expression [src] 
 2      2      
y  + 4*q  + q*y
$$4 q^{2} + q y + y^{2}$$ 
y^2 + 4*q^2 + q*y
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