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Expression simplification/ Factor perfect squares/ y^2-y*q-5*q^2

Factor y^2-y*q-5*q^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*q - 5*q
$$- 5 q^{2} + \left(- q y + y^{2}\right)$$ 
y^2 - y*q - 5*q^2
General simplification [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    y*\-1 + \/ 21 /| |    y*\1 + \/ 21 /|
|q - ---------------|*|q + --------------|
\           10      / \          10      /
$$\left(q - \frac{y \left(-1 + \sqrt{21}\right)}{10}\right) \left(q + \frac{y \left(1 + \sqrt{21}\right)}{10}\right)$$ 
(q - y*(-1 + sqrt(21))/10)*(q + y*(1 + sqrt(21))/10)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 q^{2} + \left(- q y + y^{2}\right)$$
Let us write down the identical expression
$$- 5 q^{2} + \left(- q y + y^{2}\right) = \frac{21 y^{2}}{20} + \left(- 5 q^{2} - q y - \frac{y^{2}}{20}\right)$$
or
$$- 5 q^{2} + \left(- q y + y^{2}\right) = \frac{21 y^{2}}{20} - \left(\sqrt{5} q + \frac{\sqrt{5} y}{10}\right)^{2}$$
Numerical answer [src] 
y^2 - 5.0*q^2 - q*y
y^2 - 5.0*q^2 - q*y
Trigonometric part [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Combining rational expressions [src] 
     2            
- 5*q  + y*(y - q)
$$- 5 q^{2} + y \left(- q + y\right)$$ 
-5*q^2 + y*(y - q)
Assemble expression [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Powers [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Combinatorics [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Rational denominator [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
Common denominator [src] 
 2      2      
y  - 5*q  - q*y
$$- 5 q^{2} - q y + y^{2}$$ 
y^2 - 5*q^2 - q*y
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