/ / ___\\ / / ___\\
| y*\1 - 3*I*\/ 3 /| | y*\1 + 3*I*\/ 3 /|
|t - -----------------|*|t - -----------------|
\ 14 / \ 14 /
$$\left(t - \frac{y \left(1 - 3 \sqrt{3} i\right)}{14}\right) \left(t - \frac{y \left(1 + 3 \sqrt{3} i\right)}{14}\right)$$
(t - y*(1 - 3*i*sqrt(3))/14)*(t - y*(1 + 3*i*sqrt(3))/14)
The perfect square
Let's highlight the perfect square of the square three-member
$$7 t^{2} + \left(- t y + y^{2}\right)$$
Let us write down the identical expression
$$7 t^{2} + \left(- t y + y^{2}\right) = \frac{27 y^{2}}{28} + \left(7 t^{2} - t y + \frac{y^{2}}{28}\right)$$
or
$$7 t^{2} + \left(- t y + y^{2}\right) = \frac{27 y^{2}}{28} + \left(\sqrt{7} t - \frac{\sqrt{7} y}{14}\right)^{2}$$
General simplification
[src]
$$7 t^{2} - t y + y^{2}$$
$$7 t^{2} - t y + y^{2}$$
$$7 t^{2} - t y + y^{2}$$
Assemble expression
[src]
$$7 t^{2} - t y + y^{2}$$
Rational denominator
[src]
$$7 t^{2} - t y + y^{2}$$
$$7 t^{2} - t y + y^{2}$$
Combining rational expressions
[src]
$$7 t^{2} + y \left(- t + y\right)$$
$$7 t^{2} - t y + y^{2}$$