The perfect square
Let's highlight the perfect square of the square three-member
$$- 6 x^{2} + \left(- x 4 y + y^{2}\right)$$
Let us write down the identical expression
$$- 6 x^{2} + \left(- x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} + \left(- 6 x^{2} - 4 x y - \frac{2 y^{2}}{3}\right)$$
or
$$- 6 x^{2} + \left(- x 4 y + y^{2}\right) = \frac{5 y^{2}}{3} - \left(\sqrt{6} x + \frac{\sqrt{6} y}{3}\right)^{2}$$
General simplification
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$$- 6 x^{2} - 4 x y + y^{2}$$
/ / ____\\ / / ____\\
| y*\-2 + \/ 10 /| | y*\2 + \/ 10 /|
|x - ---------------|*|x + --------------|
\ 6 / \ 6 /
$$\left(x - \frac{y \left(-2 + \sqrt{10}\right)}{6}\right) \left(x + \frac{y \left(2 + \sqrt{10}\right)}{6}\right)$$
(x - y*(-2 + sqrt(10))/6)*(x + y*(2 + sqrt(10))/6)
$$- 6 x^{2} - 4 x y + y^{2}$$
$$- 6 x^{2} - 4 x y + y^{2}$$
Assemble expression
[src]
$$- 6 x^{2} - 4 x y + y^{2}$$
Rational denominator
[src]
$$- 6 x^{2} - 4 x y + y^{2}$$
$$- 6 x^{2} - 4 x y + y^{2}$$
$$- 6 x^{2} - 4 x y + y^{2}$$
Combining rational expressions
[src]
$$- 6 x^{2} + y \left(- 4 x + y\right)$$