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

Factor -y^2+y*p-4*p^2 squared

An expression to simplify:

The solution

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