$$- 2 c^{3} - 6 c d + 8 d^{2}$$
Разложение на множители
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/ _________________________________ \ / _________________________________ \ / _________________________________ \
| / ____________________ | | / ____________________ | | / ____________________ |
| / / 3 4 | | / / 3 4 / ___\ | | / / 3 4 / ___\ |
| / \/ 2916*d + 11664*d 2 | | / \/ 2916*d + 11664*d 2 | 1 I*\/ 3 | | | / \/ 2916*d + 11664*d 2 | 1 I*\/ 3 | |
| 3 / ----------------------- - 54*d | | 3 / ----------------------- - 54*d *|- - - -------| | | 3 / ----------------------- - 54*d *|- - + -------| |
| \/ 2 3*d | | \/ 2 \ 2 2 / 3*d | | \/ 2 \ 2 2 / 3*d |
1*|c + --------------------------------------- - ---------------------------------------|*|c + ------------------------------------------------------- - -------------------------------------------------------|*|c + ------------------------------------------------------- - -------------------------------------------------------|
| 3 _________________________________| | 3 _________________________________| | 3 _________________________________|
| / ____________________ | | / ____________________ | | / ____________________ |
| / / 3 4 | | / ___\ / / 3 4 | | / ___\ / / 3 4 |
| / \/ 2916*d + 11664*d 2 | | | 1 I*\/ 3 | / \/ 2916*d + 11664*d 2 | | | 1 I*\/ 3 | / \/ 2916*d + 11664*d 2 |
| 3 / ----------------------- - 54*d | | |- - - -------|*3 / ----------------------- - 54*d | | |- - + -------|*3 / ----------------------- - 54*d |
\ \/ 2 / \ \ 2 2 / \/ 2 / \ \ 2 2 / \/ 2 /
$$1 \left(c - \left(- \frac{\sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}{3} + \frac{3 d}{\sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}\right)\right) \left(c - \left(- \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}{3} + \frac{3 d}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}\right)\right) \left(c - \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}{3} + \frac{3 d}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- 54 d^{2} + \frac{\sqrt{11664 d^{4} + 2916 d^{3}}}{2}}}\right)\right)$$
((1*(c + ((sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3)/3 - 3*d/(sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3))))*(c + ((sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 3*d/((-1/2 - i*sqrt(3)/2)*(sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3)))))*(c + ((sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 3*d/((-1/2 + i*sqrt(3)/2)*(sqrt(2916*d^3 + 11664*d^4)/2 - 54*d^2)^(1/3))))
Подстановка условия
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-5*c^3 - 2*d^2 - 3*c*d - 3*c*d + 3*c^3 + 10*d^2 при c = 2
3 2 3 2
- 5*c - 2*d - 3*c*d - 3*c*d + 3*c + 10*d
$$- 5 c^{3} + 3 c^{3} - 3 c d - 3 c d - 2 d^{2} + 10 d^{2}$$
$$- 2 c^{3} - 6 c d + 8 d^{2}$$
$$c = 2$$
3 2
- 2*(2) + 8*d - 6*(2)*d
$$- 2 (2)^{3} - 6 (2) d + 8 d^{2}$$
$$8 d^{2} - 12 d - 2 \cdot 2^{3}$$
$$8 d^{2} - 12 d - 16$$
8.0*d^2 - 2.0*c^3 - 6.0*c*d
8.0*d^2 - 2.0*c^3 - 6.0*c*d
$$- 2 c^{3} - 6 c d + 8 d^{2}$$
Объединение рациональных выражений
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/ 3 2 \
2*\- c + 4*d - 3*c*d/
$$2 \left(- c^{3} - 3 c d + 4 d^{2}\right)$$
Рациональный знаменатель
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$$- 2 c^{3} - 6 c d + 8 d^{2}$$
$$- 2 c^{3} - 6 c d + 8 d^{2}$$
$$- 2 c^{3} - 6 c d + 8 d^{2}$$
$$- 2 c^{3} - 6 c d + 8 d^{2}$$