/ y*(-1 + I)\ / y*(1 + I)\
|p - ----------|*|p + ---------|
\ 2 / \ 2 /
$$\left(p - \frac{y \left(-1 + i\right)}{2}\right) \left(p + \frac{y \left(1 + i\right)}{2}\right)$$
(p - y*(-1 + i)/2)*(p + y*(1 + i)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 2 p^{2} + \left(- p 2 y - y^{2}\right)$$
Let us write down the identical expression
$$- 2 p^{2} + \left(- p 2 y - y^{2}\right) = - \frac{y^{2}}{2} + \left(- 2 p^{2} - 2 p y - \frac{y^{2}}{2}\right)$$
or
$$- 2 p^{2} + \left(- p 2 y - y^{2}\right) = - \frac{y^{2}}{2} - \left(\sqrt{2} p + \frac{\sqrt{2} y}{2}\right)^{2}$$
General simplification
[src]
$$- 2 p^{2} - 2 p y - y^{2}$$
$$- 2 p^{2} - 2 p y - y^{2}$$
Rational denominator
[src]
$$- 2 p^{2} - 2 p y - y^{2}$$
$$- 2 p^{2} - 2 p y - y^{2}$$
Assemble expression
[src]
$$- 2 p^{2} - 2 p y - y^{2}$$
$$- 2 p^{2} - 2 p y - y^{2}$$
Combining rational expressions
[src]
$$- 2 p^{2} + y \left(- 2 p - y\right)$$
$$- 2 p^{2} - 2 p y - y^{2}$$