Общий множитель 49*m^22-60*m^11*n^8+16*n^16

Объединение рациональных выражений

    16    11 /      8       11\
16*n   + m  *\- 60*n  + 49*m  /

$$m^{11} \left(49 m^{11} - 60 n^{8}\right) + 16 n^{16}$$

Комбинаторика

    16       22       11  8
16*n   + 49*m   - 60*m  *n 

$$49 m^{22} - 60 m^{11} n^{8} + 16 n^{16}$$

Разложение на множители

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|        /     8       ____  8 | |        /     8       ____  8 | |        /     8       ____  8                  /     8       ____  8         | |        /     8       ____  8                  /     8       ____  8         | |          /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                  /     8       ____  8         | |        /     8       ____  8                  /     8       ____  8         | |          /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |          /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           | |        /     8       ____  8                    /     8       ____  8           |
|       /  30*n    2*\/ 29 *n  | |       /  30*n    2*\/ 29 *n  | |       /  30*n    2*\/ 29 *n      /pi\        /  30*n    2*\/ 29 *n      /pi\| |       /  30*n    2*\/ 29 *n      /pi\        /  30*n    2*\/ 29 *n      /pi\| |         /  30*n    2*\/ 29 *n      /2*pi\        /  30*n    2*\/ 29 *n      /2*pi\| |         /  30*n    2*\/ 29 *n      /2*pi\        /  30*n    2*\/ 29 *n      /2*pi\| |       /  30*n    2*\/ 29 *n      /3*pi\        /  30*n    2*\/ 29 *n      /3*pi\| |       /  30*n    2*\/ 29 *n      /3*pi\        /  30*n    2*\/ 29 *n      /3*pi\| |         /  30*n    2*\/ 29 *n      /4*pi\        /  30*n    2*\/ 29 *n      /4*pi\| |         /  30*n    2*\/ 29 *n      /4*pi\        /  30*n    2*\/ 29 *n      /4*pi\| |       /  30*n    2*\/ 29 *n      /5*pi\        /  30*n    2*\/ 29 *n      /5*pi\| |       /  30*n    2*\/ 29 *n      /5*pi\        /  30*n    2*\/ 29 *n      /5*pi\| |       /  30*n    2*\/ 29 *n      /pi\        /  30*n    2*\/ 29 *n      /pi\| |       /  30*n    2*\/ 29 *n      /pi\        /  30*n    2*\/ 29 *n      /pi\| |         /  30*n    2*\/ 29 *n      /2*pi\        /  30*n    2*\/ 29 *n      /2*pi\| |         /  30*n    2*\/ 29 *n      /2*pi\        /  30*n    2*\/ 29 *n      /2*pi\| |       /  30*n    2*\/ 29 *n      /3*pi\        /  30*n    2*\/ 29 *n      /3*pi\| |       /  30*n    2*\/ 29 *n      /3*pi\        /  30*n    2*\/ 29 *n      /3*pi\| |         /  30*n    2*\/ 29 *n      /4*pi\        /  30*n    2*\/ 29 *n      /4*pi\| |         /  30*n    2*\/ 29 *n      /4*pi\        /  30*n    2*\/ 29 *n      /4*pi\| |       /  30*n    2*\/ 29 *n      /5*pi\        /  30*n    2*\/ 29 *n      /5*pi\| |       /  30*n    2*\/ 29 *n      /5*pi\        /  30*n    2*\/ 29 *n      /5*pi\|
|m - 11/   ----- - ----------- |*|m - 11/   ----- + ----------- |*|m + 11/   ----- - ----------- *cos|--| + I*11/   ----- - ----------- *sin|--||*|m + 11/   ----- - ----------- *cos|--| - I*11/   ----- - ----------- *sin|--||*|m + - 11/   ----- - ----------- *cos|----| + I*11/   ----- - ----------- *sin|----||*|m + - 11/   ----- - ----------- *cos|----| - I*11/   ----- - ----------- *sin|----||*|m + 11/   ----- - ----------- *cos|----| + I*11/   ----- - ----------- *sin|----||*|m + 11/   ----- - ----------- *cos|----| - I*11/   ----- - ----------- *sin|----||*|m + - 11/   ----- - ----------- *cos|----| + I*11/   ----- - ----------- *sin|----||*|m + - 11/   ----- - ----------- *cos|----| - I*11/   ----- - ----------- *sin|----||*|m + 11/   ----- - ----------- *cos|----| + I*11/   ----- - ----------- *sin|----||*|m + 11/   ----- - ----------- *cos|----| - I*11/   ----- - ----------- *sin|----||*|m + 11/   ----- + ----------- *cos|--| + I*11/   ----- + ----------- *sin|--||*|m + 11/   ----- + ----------- *cos|--| - I*11/   ----- + ----------- *sin|--||*|m + - 11/   ----- + ----------- *cos|----| + I*11/   ----- + ----------- *sin|----||*|m + - 11/   ----- + ----------- *cos|----| - I*11/   ----- + ----------- *sin|----||*|m + 11/   ----- + ----------- *cos|----| + I*11/   ----- + ----------- *sin|----||*|m + 11/   ----- + ----------- *cos|----| - I*11/   ----- + ----------- *sin|----||*|m + - 11/   ----- + ----------- *cos|----| + I*11/   ----- + ----------- *sin|----||*|m + - 11/   ----- + ----------- *cos|----| - I*11/   ----- + ----------- *sin|----||*|m + 11/   ----- + ----------- *cos|----| + I*11/   ----- + ----------- *sin|----||*|m + 11/   ----- + ----------- *cos|----| - I*11/   ----- + ----------- *sin|----||
\    \/      49         49     / \    \/      49         49     / \    \/      49         49         \11/     \/      49         49         \11// \    \/      49         49         \11/     \/      49         49         \11// \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \11/     \/      49         49         \11// \    \/      49         49         \11/     \/      49         49         \11// \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \      \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 // \    \/      49         49         \ 11 /     \/      49         49         \ 11 //

$$\left(m - \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}}\right) \left(m - \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}}\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{\pi}{11} \right)} + i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{\pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{\pi}{11} \right)} - i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{\pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{2 \pi}{11} \right)} + i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{2 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{2 \pi}{11} \right)} - i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{2 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{3 \pi}{11} \right)} + i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{3 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{3 \pi}{11} \right)} - i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{3 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{4 \pi}{11} \right)} + i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{4 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{4 \pi}{11} \right)} - i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{4 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{5 \pi}{11} \right)} + i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{5 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{5 \pi}{11} \right)} - i \sqrt[11]{- \frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{5 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{\pi}{11} \right)} + i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{\pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{\pi}{11} \right)} - i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{\pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{2 \pi}{11} \right)} + i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{2 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{2 \pi}{11} \right)} - i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{2 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{3 \pi}{11} \right)} + i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{3 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{3 \pi}{11} \right)} - i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{3 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{4 \pi}{11} \right)} + i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{4 \pi}{11} \right)}\right)\right) \left(m + \left(- \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{4 \pi}{11} \right)} - i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{4 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{5 \pi}{11} \right)} + i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{5 \pi}{11} \right)}\right)\right) \left(m + \left(\sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \cos{\left(\frac{5 \pi}{11} \right)} - i \sqrt[11]{\frac{2 \sqrt{29} n^{8}}{49} + \frac{30 n^{8}}{49}} \sin{\left(\frac{5 \pi}{11} \right)}\right)\right)$$

Общее упрощение

    16       22       11  8
16*n   + 49*m   - 60*m  *n 

$$49 m^{22} - 60 m^{11} n^{8} + 16 n^{16}$$

Собрать выражение

    16       22       11  8
16*n   + 49*m   - 60*m  *n 

$$49 m^{22} - 60 m^{11} n^{8} + 16 n^{16}$$