Разложение на множители
[src]/ _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________ \
| / _________________________________________________________________________ | | / _________________________________________________________________________ | | / _________________________________________________________________________ |
| / / 2 3 | | / / 2 3 | | / / 2 3 |
| / / / 3 3 3 \ / 2 2 \ | | / / / 3 3 3 \ / 2 2 \ | | / / / 3 3 3 \ / 2 2 \ |
| / / | 81*y 54*y 27*y | | 9*y 9*y | | | / / | 81*y 54*y 27*y | | 9*y 9*y | | | / / | 81*y 54*y 27*y | | 9*y 9*y | |
| / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| | | / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| | | / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| |
| / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 2 2 | | / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 / ___\ 2 2 | | / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 / ___\ 2 2 |
| / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y 9*y 9*y | | / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y | 1 I*\/ 3 | 9*y 9*y | | / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y | 1 I*\/ 3 | 9*y 9*y |
| / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ -------- + ----------- | | / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ *|- - - -------| -------- + ----------- | | / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ *|- - + -------| -------- + ----------- |
| 3 / 2 3 2 2*(-1 + 2*y) -1 + 2*y 2 | | 3 / 2 3 2 2*(-1 + 2*y) \ 2 2 / -1 + 2*y 2 | | 3 / 2 3 2 2*(-1 + 2*y) \ 2 2 / -1 + 2*y 2 |
| \/ (-1 + 2*y) 2*(-1 + 2*y) y (-1 + 2*y) | | y \/ (-1 + 2*y) 2*(-1 + 2*y) (-1 + 2*y) | | y \/ (-1 + 2*y) 2*(-1 + 2*y) (-1 + 2*y) |
|x + ------------------------------------------------------------------------------------------------------------------------------------------ - -------- + --------------------------------------------------------------------------------------------------------------------------------------------|*|x + - -------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - -------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 3 -1 + 2*y _______________________________________________________________________________________________________________________________| | -1 + 2*y 3 _______________________________________________________________________________________________________________________________| | -1 + 2*y 3 _______________________________________________________________________________________________________________________________|
| / _________________________________________________________________________ | | / _________________________________________________________________________ | | / _________________________________________________________________________ |
| / / 2 3 | | / / 2 3 | | / / 2 3 |
| / / / 3 3 3 \ / 2 2 \ | | / / / 3 3 3 \ / 2 2 \ | | / / / 3 3 3 \ / 2 2 \ |
| / / | 81*y 54*y 27*y | | 9*y 9*y | | | / / | 81*y 54*y 27*y | | 9*y 9*y | | | / / | 81*y 54*y 27*y | | 9*y 9*y | |
| / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| | | / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| | | / / |- ----------- - ----------- - --------| - 4*|-------- + -----------| |
| / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 | | / ___\ / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 | | / ___\ / / | 2 3 -1 + 2*y| |-1 + 2*y 2| 3 3 3 |
| / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y | | | 1 I*\/ 3 | / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y | | | 1 I*\/ 3 | / \/ \ (-1 + 2*y) (-1 + 2*y) / \ (-1 + 2*y) / 27*y 81*y 27*y |
| 3* / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ | | 3*|- - - -------|* / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ | | 3*|- - + -------|* / -------------------------------------------------------------------------------- - ----------- - ------------- - ------------ |
| 3 / 2 3 2 2*(-1 + 2*y) | | \ 2 2 / 3 / 2 3 2 2*(-1 + 2*y) | | \ 2 2 / 3 / 2 3 2 2*(-1 + 2*y) |
\ \/ (-1 + 2*y) 2*(-1 + 2*y) / \ \/ (-1 + 2*y) 2*(-1 + 2*y) / \ \/ (-1 + 2*y) 2*(-1 + 2*y) /
$$\left(x + \left(- \frac{y}{2 y - 1} + \frac{\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}}{3 \sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}} + \frac{\sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}}{3}\right)\right) \left(x + \left(- \frac{y}{2 y - 1} + \frac{\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}}{3}\right)\right) \left(x + \left(- \frac{y}{2 y - 1} + \frac{\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 y^{3}}{2 \left(2 y - 1\right)} - \frac{81 y^{3}}{2 \left(2 y - 1\right)^{2}} - \frac{27 y^{3}}{\left(2 y - 1\right)^{3}} + \frac{\sqrt{- 4 \left(\frac{9 y^{2}}{2 y - 1} + \frac{9 y^{2}}{\left(2 y - 1\right)^{2}}\right)^{3} + \left(- \frac{27 y^{3}}{2 y - 1} - \frac{81 y^{3}}{\left(2 y - 1\right)^{2}} - \frac{54 y^{3}}{\left(2 y - 1\right)^{3}}\right)^{2}}}{2}}}{3}\right)\right)$$
3 3 2 2
- y + x *(-1 + 2*y) - 3*x*y - 3*y*x
$$x^{3} \left(2 y - 1\right) - 3 x^{2} y - 3 x y^{2} - y^{3}$$
3 3 / 2 3\ 2
- x - y + y*\- 3*x + 2*x / - 3*x*y
$$- x^{3} - 3 x y^{2} - y^{3} + y \left(2 x^{3} - 3 x^{2}\right)$$
3 3 2 2 3
- x - y - 3*x*y - 3*y*x + 2*y*x
$$2 x^{3} y - x^{3} - 3 x^{2} y - 3 x y^{2} - y^{3}$$