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Раскрыть скобки в (5*a^8-6*x^3)*(5*a^8+6*x^3)

Выражение, которое надо упростить:

Решение

Вы ввели [src]
/   8      3\ /   8      3\
\5*a  - 6*x /*\5*a  + 6*x /
$$\left(5 a^{8} + 6 x^{3}\right) \left(5 a^{8} - 6 x^{3}\right)$$
(5*a^8 - 6*x^3)*(5*a^8 + 6*x^3)
Разложение на множители [src]
  /                  _____\ /                  _____\ /                  ____\ /                  ____\ /                    _____\ /                    _____\ /                    ____\ /                    ____\ /                       _____                        _____\ /                       _____                        _____\ /                         _____                        _____\ /                         _____                        _____\ /                       ____                        ____\ /                       ____                        ____\ /                         ____                        ____\ /                         ____                        ____\
  |     7/8 8 ___ 8 /   3 | |     7/8 8 ___ 8 /   3 | |     7/8 8 ___ 8 /  3 | |     7/8 8 ___ 8 /  3 | |       7/8 8 ___ 8 /   3 | |       7/8 8 ___ 8 /   3 | |       7/8 8 ___ 8 /  3 | |       7/8 8 ___ 8 /  3 | |     5/8 8 ___  7/8 8 /   3       5/8 8 ___  7/8 8 /   3 | |     5/8 8 ___  7/8 8 /   3       5/8 8 ___  7/8 8 /   3 | |       5/8 8 ___  7/8 8 /   3       5/8 8 ___  7/8 8 /   3 | |       5/8 8 ___  7/8 8 /   3       5/8 8 ___  7/8 8 /   3 | |     5/8 8 ___  7/8 8 /  3       5/8 8 ___  7/8 8 /  3 | |     5/8 8 ___  7/8 8 /  3       5/8 8 ___  7/8 8 /  3 | |       5/8 8 ___  7/8 8 /  3       5/8 8 ___  7/8 8 /  3 | |       5/8 8 ___  7/8 8 /  3       5/8 8 ___  7/8 8 /  3 |
  |    5   *\/ 6 *\/  -x  | |    5   *\/ 6 *\/  -x  | |    5   *\/ 6 *\/  x  | |    5   *\/ 6 *\/  x  | |    I*5   *\/ 6 *\/  -x  | |    I*5   *\/ 6 *\/  -x  | |    I*5   *\/ 6 *\/  x  | |    I*5   *\/ 6 *\/  x  | |    2   *\/ 3 *5   *\/  -x     I*2   *\/ 3 *5   *\/  -x  | |    2   *\/ 3 *5   *\/  -x     I*2   *\/ 3 *5   *\/  -x  | |      2   *\/ 3 *5   *\/  -x     I*2   *\/ 3 *5   *\/  -x  | |      2   *\/ 3 *5   *\/  -x     I*2   *\/ 3 *5   *\/  -x  | |    2   *\/ 3 *5   *\/  x     I*2   *\/ 3 *5   *\/  x  | |    2   *\/ 3 *5   *\/  x     I*2   *\/ 3 *5   *\/  x  | |      2   *\/ 3 *5   *\/  x     I*2   *\/ 3 *5   *\/  x  | |      2   *\/ 3 *5   *\/  x     I*2   *\/ 3 *5   *\/  x  |
1*|a + -------------------|*|a - -------------------|*|a + ------------------|*|a - ------------------|*|a + ---------------------|*|a - ---------------------|*|a + --------------------|*|a - --------------------|*|a + ------------------------ + --------------------------|*|a + ------------------------ - --------------------------|*|a + - ------------------------ + --------------------------|*|a + - ------------------------ - --------------------------|*|a + ----------------------- + -------------------------|*|a + ----------------------- - -------------------------|*|a + - ----------------------- + -------------------------|*|a + - ----------------------- - -------------------------|
  \             5         / \             5         / \            5         / \            5         / \              5          / \              5          / \             5          / \             5          / \               10                          10            / \               10                          10            / \                 10                          10            / \                 10                          10            / \               10                         10           / \               10                         10           / \                 10                         10           / \                 10                         10           /
$$\left(a - \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} \sqrt[8]{- x^{3}}}{5}\right) 1 \left(a + \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} \sqrt[8]{- x^{3}}}{5}\right) \left(a + \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} \sqrt[8]{x^{3}}}{5}\right) \left(a - \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} \sqrt[8]{x^{3}}}{5}\right) \left(a + \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} i \sqrt[8]{- x^{3}}}{5}\right) \left(a - \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} i \sqrt[8]{- x^{3}}}{5}\right) \left(a + \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} i \sqrt[8]{x^{3}}}{5}\right) \left(a - \frac{5^{\frac{7}{8}} \cdot \sqrt[8]{6} i \sqrt[8]{x^{3}}}{5}\right) \left(a + \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{- x^{3}}}{10} + \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{- x^{3}}}{10}\right)\right) \left(a + \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{- x^{3}}}{10} - \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{- x^{3}}}{10}\right)\right) \left(a - \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{- x^{3}}}{10} - \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{- x^{3}}}{10}\right)\right) \left(a - \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{- x^{3}}}{10} + \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{- x^{3}}}{10}\right)\right) \left(a + \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{x^{3}}}{10} + \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{x^{3}}}{10}\right)\right) \left(a + \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{x^{3}}}{10} - \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{x^{3}}}{10}\right)\right) \left(a - \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{x^{3}}}{10} - \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{x^{3}}}{10}\right)\right) \left(a - \left(\frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} \sqrt[8]{x^{3}}}{10} + \frac{2^{\frac{5}{8}} \cdot \sqrt[8]{3} \cdot 5^{\frac{7}{8}} i \sqrt[8]{x^{3}}}{10}\right)\right)$$
(((((((((((((((1*(a + 5^(7/8)*6^(1/8)*(-x^3)^(1/8)/5))*(a - 5^(7/8)*6^(1/8)*(-x^3)^(1/8)/5))*(a + 5^(7/8)*6^(1/8)*(x^3)^(1/8)/5))*(a - 5^(7/8)*6^(1/8)*(x^3)^(1/8)/5))*(a + i*5^(7/8)*6^(1/8)*(-x^3)^(1/8)/5))*(a - i*5^(7/8)*6^(1/8)*(-x^3)^(1/8)/5))*(a + i*5^(7/8)*6^(1/8)*(x^3)^(1/8)/5))*(a - i*5^(7/8)*6^(1/8)*(x^3)^(1/8)/5))*(a + (2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10 + i*2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10)))*(a + (2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10 - i*2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10)))*(a - (2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10 + i*2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10)))*(a - (2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10 - i*2^(5/8)*3^(1/8)*5^(7/8)*(-x^3)^(1/8)/10)))*(a + (2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10 + i*2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10)))*(a + (2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10 - i*2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10)))*(a - (2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10 + i*2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10)))*(a - (2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10 - i*2^(5/8)*3^(1/8)*5^(7/8)*(x^3)^(1/8)/10))
Общее упрощение [src]
      6       16
- 36*x  + 25*a  
$$25 a^{16} - 36 x^{6}$$
-36*x^6 + 25*a^16
Численный ответ [src]
(6.0*x^3 + 5.0*a^8)*(5.0*a^8 - 6.0*x^3)
(6.0*x^3 + 5.0*a^8)*(5.0*a^8 - 6.0*x^3)
Общий знаменатель [src]
      6       16
- 36*x  + 25*a  
$$25 a^{16} - 36 x^{6}$$
-36*x^6 + 25*a^16
Рациональный знаменатель [src]
      6       16
- 36*x  + 25*a  
$$25 a^{16} - 36 x^{6}$$
/     3      8\ /   8      3\
\- 6*x  + 5*a /*\5*a  + 6*x /
$$\left(5 a^{8} - 6 x^{3}\right) \left(5 a^{8} + 6 x^{3}\right)$$
(-6*x^3 + 5*a^8)*(5*a^8 + 6*x^3)
Объединение рациональных выражений [src]
/     3      8\ /   8      3\
\- 6*x  + 5*a /*\5*a  + 6*x /
$$\left(5 a^{8} - 6 x^{3}\right) \left(5 a^{8} + 6 x^{3}\right)$$
(-6*x^3 + 5*a^8)*(5*a^8 + 6*x^3)
Комбинаторика [src]
 /     8      3\ /   8      3\
-\- 5*a  + 6*x /*\5*a  + 6*x /
$$- \left(- 5 a^{8} + 6 x^{3}\right) \left(5 a^{8} + 6 x^{3}\right)$$
-(-5*a^8 + 6*x^3)*(5*a^8 + 6*x^3)
Степени [src]
/     3      8\ /   8      3\
\- 6*x  + 5*a /*\5*a  + 6*x /
$$\left(5 a^{8} - 6 x^{3}\right) \left(5 a^{8} + 6 x^{3}\right)$$
(-6*x^3 + 5*a^8)*(5*a^8 + 6*x^3)
Собрать выражение [src]
/     3      8\ /   8      3\
\- 6*x  + 5*a /*\5*a  + 6*x /
$$\left(5 a^{8} - 6 x^{3}\right) \left(5 a^{8} + 6 x^{3}\right)$$
(-6*x^3 + 5*a^8)*(5*a^8 + 6*x^3)