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a^8-4*a^2-8*a-4еслиa=1/4 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
 8      2          
a  - 4*a  - 8*a - 4
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Подстановка условия [src]
a^8 - 4*a^2 - 8*a - 1*4 при a = 1/4
подставляем
 8      2          
a  - 4*a  - 8*a - 4
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
      8            2
-4 + a  - 8*a - 4*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
переменные
a = 1/4
a=14a = \frac{1}{4}
          8                    2
-4 + (1/4)  - 8*(1/4) - 4*(1/4)
(1/4)8−4(1/4)2−8(1/4)−4(1/4)^{8} - 4 (1/4)^{2} - 8 (1/4) - 4
     1              1 
-4 + -- - 8*1/4 - 4*--
      8              2
     4              4
−4−2−416+(14)8-4 - 2 - \frac{4}{16} + \left(\frac{1}{4}\right)^{8}
-409599 
--------
 65536
−40959965536- \frac{409599}{65536}
Степени [src]
      8            2
-4 + a  - 8*a - 4*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Численный ответ [src]
-4.0 + a^8 - 4.0*a^2 - 8.0*a
Рациональный знаменатель [src]
      8            2
-4 + a  - 8*a - 4*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Объединение рациональных выражений [src]
       /       /      6\\
-4 + a*\-8 + a*\-4 + a //
a(a(a6−4)−8)−4a \left(a \left(a^{6} - 4\right) - 8\right) - 4
Общее упрощение [src]
      8            2
-4 + a  - 8*a - 4*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Собрать выражение [src]
      8      2      
-4 + a  - 4*a  - 8*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Комбинаторика [src]
/      4      \ /     4      \
\-2 + a  - 2*a/*\2 + a  + 2*a/
(a4−2a−2)(a4+2a+2)\left(a^{4} - 2 a - 2\right) \left(a^{4} + 2 a + 2\right)
Общий знаменатель [src]
      8            2
-4 + a  - 8*a - 4*a
a8−4a2−8a−4a^{8} - 4 a^{2} - 8 a - 4
Разложение на множители [src]
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  |                                                                          /                                4                                   /  1   \/ 465              4           | |                  /                                4                                   /  1   \/ 465              4                                                                     | |                                                                            /          /  1   \/ 465                                4                                       4           | |                                                                              /          /  1   I*\/ 303                                  4                                          4            | |                                                                                /                                  4                                     /  1   I*\/ 303               4            | |                                                                            /          /  1   \/ 465                                4                                       4           | |                                                                                /                                  4                                     /  1   I*\/ 303               4            | |                  /          /  1   I*\/ 303                                  4                                          4                                                                          |
  |                                                                         /    - ------------------------------------------------------- - 2*3 /   - + -------  + -------------------- | |                 /    - ------------------------------------------------------- - 2*3 /   - + -------  + --------------------                                                           | |                                                                           /    - 2*3 /   - + -------  + ------------------------------------------------------- + -------------------- | |                                                                             /    - 2*3 /   - + ---------  + ----------------------------------------------------------- - ---------------------- | |                                                                               /    - ----------------------------------------------------------- - 2*3 /   - + ---------  - ---------------------- | |                                                                           /    - 2*3 /   - + -------  + ------------------------------------------------------- + -------------------- | |                                                                               /    - ----------------------------------------------------------- - 2*3 /   - + ---------  - ---------------------- | |                 /    - 2*3 /   - + ---------  + ----------------------------------------------------------- - ----------------------                                                               |
  |              _____________________________________________             /                 _____________________________________________     \/    4      36             _____________ | |                /                 _____________________________________________     \/    4      36             _____________              _____________________________________________| |                _____________________________________________             /         \/    4      36                _____________________________________________          _____________ | |              _________________________________________________             /         \/    4       36                 _________________________________________________          _______________ | |                _________________________________________________             /                 _________________________________________________     \/    4       36              _______________ | |                _____________________________________________             /         \/    4      36                _____________________________________________          _____________ | |                _________________________________________________             /                 _________________________________________________     \/    4       36              _______________ | |                /         \/    4       36                 _________________________________________________          _______________              _________________________________________________|
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  |            /        /       _____                                    /                 /        /       _____                                                        /  1   \/ 465   | |              /                 /        /       _____                                                        /  1   \/ 465              /        /       _____                         | |              /        /       _____                                    /                                        /        /       _____                                 /  1   \/ 465   | |            /        /         _____                                      /                                          /        /         _____                                   /  1   I*\/ 303   | |              /        /         _____                                      /                 /        /         _____                                                            /  1   I*\/ 303   | |              /        /       _____                                    /                                        /        /       _____                                 /  1   \/ 465   | |              /        /         _____                                      /                 /        /         _____                                                            /  1   I*\/ 303   | |              /                                          /        /         _____                                   /  1   I*\/ 303              /        /         _____                           |
  |           /        /  1   \/ 465              4                     /                 /        /  1   \/ 465              4                                     3*3 /   - + -------  | |             /                 /        /  1   \/ 465              4                                     3*3 /   - + -------            /        /  1   \/ 465              4           | |             /        /  1   \/ 465              4                     /                                        /        /  1   \/ 465              4              3*3 /   - + -------  | |           /        /  1   I*\/ 303               4                      /                                          /        /  1   I*\/ 303               4               3*3 /   - + ---------  | |             /        /  1   I*\/ 303               4                      /                 /        /  1   I*\/ 303               4                                        3*3 /   - + ---------  | |             /        /  1   \/ 465              4                     /                                        /        /  1   \/ 465              4              3*3 /   - + -------  | |             /        /  1   I*\/ 303               4                      /                 /        /  1   I*\/ 303               4                                        3*3 /   - + ---------  | |             /                                          /        /  1   I*\/ 303               4               3*3 /   - + ---------            /        /  1   I*\/ 303               4            |
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  |         /       \/    4      36             _____________         /                 /       \/    4      36             _____________                                                | |           /                 /       \/    4      36             _____________                                                        /       \/    4      36             _____________ | |           /       \/    4      36             _____________         /                                        /       \/    4      36             _____________                         | |         /       \/    4       36              _______________         /                                          /       \/    4       36              _______________                           | |           /       \/    4       36              _______________         /                 /       \/    4       36              _______________                                                    | |           /       \/    4      36             _____________         /                                        /       \/    4      36             _____________                         | |           /       \/    4       36              _______________         /                 /       \/    4       36              _______________                                                    | |           /                                          /       \/    4       36              _______________                                   /       \/    4       36              _______________ |
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  |       /                                   /  1   \/ 465         /                 /                                   /  1   \/ 465                                                  | |         /                 /                                   /  1   \/ 465                                                        /                                   /  1   \/ 465   | |         /                                   /  1   \/ 465         /                                        /                                   /  1   \/ 465                           | |       /                                     /  1   I*\/ 303         /                                          /                                     /  1   I*\/ 303                             | |         /                                     /  1   I*\/ 303         /                 /                                     /  1   I*\/ 303                                                      | |         /                                   /  1   \/ 465         /                                        /                                   /  1   \/ 465                           | |         /                                     /  1   I*\/ 303         /                 /                                     /  1   I*\/ 303                                                      | |         /                                          /                                     /  1   I*\/ 303                                   /                                     /  1   I*\/ 303   |
  |      /                               3*3 /   - + -------       /                 /                               3*3 /   - + -------                                                 | |        /                 /                               3*3 /   - + -------                                                      /                               3*3 /   - + -------  | |        /                               3*3 /   - + -------       /                                        /                               3*3 /   - + -------                          | |      /                                 3*3 /   - + ---------       /                                          /                                 3*3 /   - + ---------                            | |        /                                 3*3 /   - + ---------       /                 /                                 3*3 /   - + ---------                                                     | |        /                               3*3 /   - + -------       /                                        /                               3*3 /   - + -------                          | |        /                                 3*3 /   - + ---------       /                 /                                 3*3 /   - + ---------                                                     | |        /                                          /                                 3*3 /   - + ---------                                 /                                 3*3 /   - + ---------  |
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(a+(−4314+465363+214+4653632−−4−4314+465363+214+465363−214+465363+4314+4653632))1(a+(−4314+465363+214+4653632+−4−4314+465363+214+465363−214+465363+4314+4653632))(a−(−4314+465363+214+4653632+−214+465363+4314+465363+4−4314+465363+214+4653632))(a+(−214+303i363+44314+303i363+214+303i363−4314+303i3632+4314+303i363+214+303i3632))(a−(4314+303i363+214+303i3632+−214+303i363−44314+303i363+214+303i363−4314+303i3632))(a−(−−214+465363+4314+465363+4−4314+465363+214+4653632+−4314+465363+214+4653632))(a−(−−214+303i363−44314+303i363+214+303i363−4314+303i3632+4314+303i363+214+303i3632))(a−(−214+303i363+44314+303i363+214+303i363−4314+303i3632−4314+303i363+214+303i3632))\left(a + \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} - \frac{\sqrt{- \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}} - 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}{2}\right)\right) 1 \left(a + \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} + \frac{\sqrt{- \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}} - 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}}{2}\right)\right) \left(a + \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} + \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} + \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} - \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2}\right)\right) \left(a - \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}} + \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + \frac{4}{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}}}{2} + \frac{\sqrt{- \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{465}}{36}}}}{2}\right)\right) \left(a - \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} - \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} + \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right) \left(a - \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}} + \frac{4}{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}} - \frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}}{2} - \frac{\sqrt{\frac{4}{3 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}} + 2 \sqrt[3]{\frac{1}{4} + \frac{\sqrt{303} i}{36}}}}{2}\right)\right)