Господин Экзамен

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Раскрыть скобки в (6*c^5-7*d^2)*(6*c^5+7*d^2)

Выражение, которое надо упростить:

Решение

Вы ввели [src]
/   5      2\ /   5      2\
\6*c  - 7*d /*\6*c  + 7*d /
$$\left(6 c^{5} + 7 d^{2}\right) \left(6 c^{5} - 7 d^{2}\right)$$
(6*c^5 - 7*d^2)*(6*c^5 + 7*d^2)
Разложение на множители [src]
                                                     /                                                                                 ___________\ /                                                                                 ___________\ /                                                                              ___________\ /                                                                              ___________\ /                                                                                 ___________\ /                                                                                 ___________\ /                                                                              ___________\ /                                                                              ___________\
                                                     |                                                                      _____     /       ___ | |                                                                      _____     /       ___ | |                                                                    ____     /       ___ | |                                                                    ____     /       ___ | |                                                                      _____     /       ___ | |                                                                      _____     /       ___ | |                                                                    ____     /       ___ | |                                                                    ____     /       ___ |
  /                  _____\ /                  ____\ |                  _____                       _____      4/5 5 ___ 5 /   2     /  5   \/ 5  | |                  _____                       _____      4/5 5 ___ 5 /   2     /  5   \/ 5  | |                  ____                       ____      4/5 5 ___ 5 /  2     /  5   \/ 5  | |                  ____                       ____      4/5 5 ___ 5 /  2     /  5   \/ 5  | |                  _____                       _____      4/5 5 ___ 5 /   2     /  5   \/ 5  | |                  _____                       _____      4/5 5 ___ 5 /   2     /  5   \/ 5  | |                  ____                       ____      4/5 5 ___ 5 /  2     /  5   \/ 5  | |                  ____                       ____      4/5 5 ___ 5 /  2     /  5   \/ 5  |
  |     4/5 5 ___ 5 /   2 | |     4/5 5 ___ 5 /  2 | |     4/5 5 ___ 5 /   2      ___  4/5 5 ___ 5 /   2    I*6   *\/ 7 *\/  -d  *  /   - + ----- | |     4/5 5 ___ 5 /   2      ___  4/5 5 ___ 5 /   2    I*6   *\/ 7 *\/  -d  *  /   - + ----- | |     4/5 5 ___ 5 /  2      ___  4/5 5 ___ 5 /  2    I*6   *\/ 7 *\/  d  *  /   - + ----- | |     4/5 5 ___ 5 /  2      ___  4/5 5 ___ 5 /  2    I*6   *\/ 7 *\/  d  *  /   - + ----- | |     4/5 5 ___ 5 /   2      ___  4/5 5 ___ 5 /   2    I*6   *\/ 7 *\/  -d  *  /   - - ----- | |     4/5 5 ___ 5 /   2      ___  4/5 5 ___ 5 /   2    I*6   *\/ 7 *\/  -d  *  /   - - ----- | |     4/5 5 ___ 5 /  2      ___  4/5 5 ___ 5 /  2    I*6   *\/ 7 *\/  d  *  /   - - ----- | |     4/5 5 ___ 5 /  2      ___  4/5 5 ___ 5 /  2    I*6   *\/ 7 *\/  d  *  /   - - ----- |
  |    6   *\/ 7 *\/  -d  | |    6   *\/ 7 *\/  d  | |    6   *\/ 7 *\/  -d     \/ 5 *6   *\/ 7 *\/  -d                           \/    8     8   | |    6   *\/ 7 *\/  -d     \/ 5 *6   *\/ 7 *\/  -d                           \/    8     8   | |    6   *\/ 7 *\/  d     \/ 5 *6   *\/ 7 *\/  d                          \/    8     8   | |    6   *\/ 7 *\/  d     \/ 5 *6   *\/ 7 *\/  d                          \/    8     8   | |    6   *\/ 7 *\/  -d     \/ 5 *6   *\/ 7 *\/  -d                           \/    8     8   | |    6   *\/ 7 *\/  -d     \/ 5 *6   *\/ 7 *\/  -d                           \/    8     8   | |    6   *\/ 7 *\/  d     \/ 5 *6   *\/ 7 *\/  d                          \/    8     8   | |    6   *\/ 7 *\/  d     \/ 5 *6   *\/ 7 *\/  d                          \/    8     8   |
1*|c - -------------------|*|c - ------------------|*|c + ------------------- - ------------------------- + --------------------------------------|*|c + ------------------- - ------------------------- - --------------------------------------|*|c + ------------------ - ------------------------ + -------------------------------------|*|c + ------------------ - ------------------------ - -------------------------------------|*|c + ------------------- + ------------------------- + --------------------------------------|*|c + ------------------- + ------------------------- - --------------------------------------|*|c + ------------------ + ------------------------ + -------------------------------------|*|c + ------------------ + ------------------------ - -------------------------------------|
  \             6         / \            6         / \             24                       24                                6                   / \             24                       24                                6                   / \            24                      24                                6                  / \            24                      24                                6                  / \             24                       24                                6                   / \             24                       24                                6                   / \            24                      24                                6                  / \            24                      24                                6                  /
$$1 \left(c - \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{6}\right) \left(c - \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{6}\right) \left(c + \left(- \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt[5]{- d^{2}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)\right) \left(c - \left(- \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt[5]{- d^{2}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)\right) \left(c + \left(- \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sqrt[5]{d^{2}}}{6}\right)\right) \left(c - \left(- \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sqrt[5]{d^{2}}}{6}\right)\right) \left(c + \left(\frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt[5]{- d^{2}} \sqrt{- \frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)\right) \left(c + \left(\frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{- d^{2}}}{24} - \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt[5]{- d^{2}} \sqrt{- \frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)\right) \left(c + \left(\frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt{- \frac{\sqrt{5}}{8} + \frac{5}{8}} \sqrt[5]{d^{2}}}{6}\right)\right) \left(c + \left(\frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} + \frac{\sqrt{5} \cdot 6^{\frac{4}{5}} \cdot \sqrt[5]{7} \sqrt[5]{d^{2}}}{24} - \frac{6^{\frac{4}{5}} \cdot \sqrt[5]{7} i \sqrt{- \frac{\sqrt{5}}{8} + \frac{5}{8}} \sqrt[5]{d^{2}}}{6}\right)\right)$$
(((((((((1*(c - 6^(4/5)*7^(1/5)*(-d^2)^(1/5)/6))*(c - 6^(4/5)*7^(1/5)*(d^2)^(1/5)/6))*(c + (6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 - sqrt(5)*6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 + i*6^(4/5)*7^(1/5)*(-d^2)^(1/5)*sqrt(5/8 + sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 - sqrt(5)*6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 - i*6^(4/5)*7^(1/5)*(-d^2)^(1/5)*sqrt(5/8 + sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 - sqrt(5)*6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 + i*6^(4/5)*7^(1/5)*(d^2)^(1/5)*sqrt(5/8 + sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 - sqrt(5)*6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 - i*6^(4/5)*7^(1/5)*(d^2)^(1/5)*sqrt(5/8 + sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 + sqrt(5)*6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 + i*6^(4/5)*7^(1/5)*(-d^2)^(1/5)*sqrt(5/8 - sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 + sqrt(5)*6^(4/5)*7^(1/5)*(-d^2)^(1/5)/24 - i*6^(4/5)*7^(1/5)*(-d^2)^(1/5)*sqrt(5/8 - sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 + sqrt(5)*6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 + i*6^(4/5)*7^(1/5)*(d^2)^(1/5)*sqrt(5/8 - sqrt(5)/8)/6)))*(c + (6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 + sqrt(5)*6^(4/5)*7^(1/5)*(d^2)^(1/5)/24 - i*6^(4/5)*7^(1/5)*(d^2)^(1/5)*sqrt(5/8 - sqrt(5)/8)/6))
Общее упрощение [src]
      4       10
- 49*d  + 36*c  
$$36 c^{10} - 49 d^{4}$$
-49*d^4 + 36*c^10
Численный ответ [src]
(6.0*c^5 + 7.0*d^2)*(6.0*c^5 - 7.0*d^2)
(6.0*c^5 + 7.0*d^2)*(6.0*c^5 - 7.0*d^2)
Степени [src]
/     2      5\ /   5      2\
\- 7*d  + 6*c /*\6*c  + 7*d /
$$\left(6 c^{5} - 7 d^{2}\right) \left(6 c^{5} + 7 d^{2}\right)$$
(-7*d^2 + 6*c^5)*(6*c^5 + 7*d^2)
Объединение рациональных выражений [src]
/     2      5\ /   5      2\
\- 7*d  + 6*c /*\6*c  + 7*d /
$$\left(6 c^{5} - 7 d^{2}\right) \left(6 c^{5} + 7 d^{2}\right)$$
(-7*d^2 + 6*c^5)*(6*c^5 + 7*d^2)
Общий знаменатель [src]
      4       10
- 49*d  + 36*c  
$$36 c^{10} - 49 d^{4}$$
-49*d^4 + 36*c^10
Собрать выражение [src]
/     2      5\ /   5      2\
\- 7*d  + 6*c /*\6*c  + 7*d /
$$\left(6 c^{5} - 7 d^{2}\right) \left(6 c^{5} + 7 d^{2}\right)$$
(-7*d^2 + 6*c^5)*(6*c^5 + 7*d^2)
Комбинаторика [src]
/     2      5\ /   5      2\
\- 7*d  + 6*c /*\6*c  + 7*d /
$$\left(6 c^{5} - 7 d^{2}\right) \left(6 c^{5} + 7 d^{2}\right)$$
(-7*d^2 + 6*c^5)*(6*c^5 + 7*d^2)
Рациональный знаменатель [src]
      4       10
- 49*d  + 36*c  
$$36 c^{10} - 49 d^{4}$$
/     2      5\ /   5      2\
\- 7*d  + 6*c /*\6*c  + 7*d /
$$\left(6 c^{5} - 7 d^{2}\right) \left(6 c^{5} + 7 d^{2}\right)$$
(-7*d^2 + 6*c^5)*(6*c^5 + 7*d^2)