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Раскрытие скобок в выражении/
(x^3-1)*(x^3+1)*(x^18+1)*x^36*(x^6+x^3+1)*(x^6-x^3+1)
Раскрыть скобки в (x^3-1)*(x^3+1)*(x^18+1)*x^36*(x^6+x^3+1)*(x^6-x^3+1)
Решение
Вы ввели
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/ 3 \ / 3 \ / 18 \ 36 / 6 3 \ / 6 3 \ \x - 1/*\x + 1/*\x + 1/*x *\x + x + 1/*\x - x + 1/
$$x^{36} \left(x^{3} + 1\right) \left(x^{3} - 1\right) \left(x^{18} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right)$$
(x^3 - 1*1)*(x^3 + 1)*(x^18 + 1)*x^36*(x^6 + x^3 + 1)*(x^6 - x^3 + 1)
Разложение на множители
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/ /pi\ /pi\ ___ /pi\ ___ /pi\\ / /pi\ /pi\ ___ /pi\ ___ /pi\\ / /2*pi\ /2*pi\ ___ /2*pi\ ___ /2*pi\\ / /2*pi\ /2*pi\ ___ /2*pi\ ___ /2*pi\\ / /pi\ /pi\ ___ /pi\ ___ /pi\\ / /pi\ ___ /pi\ /pi\ ___ /pi\\ / /pi\ /pi\ ___ /pi\ ___ /pi\\ / /pi\ /pi\ ___ /pi\ ___ /pi\\ / /pi\ /pi\ ___ /pi\ ___ /pi\\ / /pi\ ___ /pi\ /pi\ ___ /pi\\ / /2*pi\ /2*pi\ ___ /2*pi\ ___ /2*pi\\ / /2*pi\ ___ /2*pi\ /2*pi\ ___ /2*pi\\
/ ___\ / ___\ / ___\ / ___\ | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|----| I*sin|----| \/ 3 *sin|----| I*\/ 3 *cos|----|| | cos|----| I*sin|----| \/ 3 *sin|----| I*\/ 3 *cos|----|| | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|--| \/ 3 *sin|--| I*sin|--| I*\/ 3 *cos|--|| | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|--| I*sin|--| \/ 3 *sin|--| I*\/ 3 *cos|--|| | cos|--| \/ 3 *sin|--| I*sin|--| I*\/ 3 *cos|--|| | cos|----| I*sin|----| \/ 3 *sin|----| I*\/ 3 *cos|----|| | cos|----| \/ 3 *sin|----| I*sin|----| I*\/ 3 *cos|----||
| 1 I*\/ 3 | | 1 I*\/ 3 | | 1 I*\/ 3 | | 1 I*\/ 3 | / /pi\ /pi\\ / /pi\ /pi\\ / /pi\ /pi\\ / /pi\ /pi\\ / /2*pi\ /2*pi\\ / /2*pi\ /2*pi\\ | \18/ \18/ \18/ \18/| | \18/ \18/ \18/ \18/| | \ 9 / \ 9 / \ 9 / \ 9 /| | \ 9 / \ 9 / \ 9 / \ 9 /| / /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\\ / /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\\ / /pi\ /2*pi\ /pi\ /2*pi\ /pi\ /2*pi\ /2*pi\ /pi\\ / /pi\ /2*pi\ /pi\ /2*pi\ /2*pi\ /pi\ /pi\ /2*pi\\ / /pi\ /4*pi\ /pi\ /4*pi\ /pi\ /4*pi\ /4*pi\ /pi\\ / /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\\ / /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\ /pi\\ / /pi\ /2*pi\ /pi\ /2*pi\ /pi\ /2*pi\ /2*pi\ /pi\\ / /pi\ /2*pi\ /pi\ /2*pi\ /pi\ /2*pi\ /2*pi\ /pi\\ / /pi\ /4*pi\ /pi\ /4*pi\ /pi\ /4*pi\ /4*pi\ /pi\\ / /pi\ /4*pi\ /pi\ /4*pi\ /pi\ /4*pi\ /4*pi\ /pi\\ / /pi\ /4*pi\ /pi\ /4*pi\ /4*pi\ /pi\ /pi\ /4*pi\\ | \18/ \18/ \18/ \18/| | \18/ \18/ \18/ \18/| | \9 / \9 / \9 / \9 /| | \9 / \9 / \9 / \9 /| | \9 / \9 / \9 / \9 /| | \9 / \9 / \9 / \9 /| | \ 9 / \ 9 / \ 9 / \ 9 /| | \ 9 / \ 9 / \ 9 / \ 9 /|
1*(x + 1)*(x + 0)*(x - 1)*|x + - + -------|*|x + - - -------|*|x + - - + -------|*|x + - - - -------|*|x + cos|--| + I*sin|--||*|x + - I*sin|--| - cos|--||*|x + I*sin|--| - cos|--||*|x + - I*sin|--| - cos|--||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + - ------- - --------- + ------------- - ---------------|*|x + - ------- - --------- - ------------- + ---------------|*|x + --------- + ----------- + --------------- - -----------------|*|x + --------- - ----------- + --------------- + -----------------|*|x + - cos|--|*cos|--| + sin|--|*sin|--| - I*cos|--|*sin|--| - I*cos|--|*sin|--||*|x + - cos|--|*cos|--| - sin|--|*sin|--| - I*cos|--|*sin|--| + I*cos|--|*sin|--||*|x + - cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| - I*cos|----|*sin|--||*|x + - cos|--|*cos|----| - sin|--|*sin|----| - I*cos|----|*sin|--| + I*cos|--|*sin|----||*|x + - cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| - I*cos|----|*sin|--||*|x + cos|--|*cos|--| + sin|--|*sin|--| - I*cos|--|*sin|--| + I*cos|--|*sin|--||*|x + - sin|--|*sin|--| + cos|--|*cos|--| + I*cos|--|*sin|--| + I*cos|--|*sin|--||*|x + cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| + I*cos|----|*sin|--||*|x + - sin|--|*sin|----| + cos|--|*cos|----| + I*cos|--|*sin|----| + I*cos|----|*sin|--||*|x + cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| + I*cos|----|*sin|--||*|x + - sin|--|*sin|----| + cos|--|*cos|----| + I*cos|--|*sin|----| + I*cos|----|*sin|--||*|x + - cos|--|*cos|----| - sin|--|*sin|----| - I*cos|----|*sin|--| + I*cos|--|*sin|----||*|x + ------- + --------- + ------------- - ---------------|*|x + ------- - ------------- + --------- + ---------------|*|x + ------- + --------- + ------------- - ---------------|*|x + ------- - --------- + ------------- + ---------------|*|x + ------- - --------- - ------------- - ---------------|*|x + ------- - ------------- + --------- + ---------------|*|x + --------- - ----------- - --------------- - -----------------|*|x + --------- - --------------- + ----------- + -----------------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ \18/ \18// \ \18/ \18// \ \9 / \9 // \ \9 / \9 // \ \ 9 / \ 9 // \ \ 9 / \ 9 // \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ \9 / \18/ \9 / \18/ \9 / \18/ \18/ \9 // \ \9 / \18/ \9 / \18/ \9 / \18/ \18/ \9 // \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \18/ \ 9 / \18/ \ 9 / \ 9 / \18/ \18/ \ 9 // \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \9 / \18/ \9 / \18/ \18/ \9 / \9 / \18// \ \9 / \18/ \9 / \18/ \9 / \18/ \18/ \9 // \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \18/ \ 9 / \18/ \ 9 / \18/ \ 9 / \ 9 / \18// \ \18/ \ 9 / \18/ \ 9 / \ 9 / \18/ \18/ \ 9 // \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 /
$$\left(x + 0\right) 1 \left(x + 1\right) \left(x - 1\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x - \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x - \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x - \left(- \frac{\sqrt{3} \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{18} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{18} \right)}}{2}\right)\right) \left(x - \left(\frac{\sqrt{3} \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{18} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{\pi}{18} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{18} \right)}}{2}\right)\right) \left(x + \left(\frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} \sin{\left(\frac{2 \pi}{9} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right) \left(x + \left(\frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} \sin{\left(\frac{2 \pi}{9} \right)}}{2} - \frac{i \sin{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right) \left(x - \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x - \left(\sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(x - \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x - \left(\sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x - \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x + \left(\sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x + \left(\sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(- \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)}\right)\right) \left(x - \left(\cos{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + \sin{\left(\frac{\pi}{18} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{18} \right)} + i \sin{\left(\frac{\pi}{18} \right)} \cos{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(\frac{\sqrt{3} \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{18} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{\pi}{18} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{18} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{18} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{18} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{18} \right)}}{2}\right)\right) \left(x + \left(\frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x + \left(\frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x - \left(- \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x - \left(- \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} \sin{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sin{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right)$$
((((((((((((((((((((((((((((((((((((1*(x + 1))*(x + 0))*(x - 1))*(x + (1/2 + i*sqrt(3)/2)))*(x + (1/2 - i*sqrt(3)/2)))*(x - (1/2 + i*sqrt(3)/2)))*(x - (1/2 - i*sqrt(3)/2)))*(x + (cos(pi/18) + i*sin(pi/18))))*(x - (i*sin(pi/18) - cos(pi/18))))*(x + (i*sin(pi/9) - cos(pi/9))))*(x - (i*sin(pi/9) - cos(pi/9))))*(x + (i*sin(2*pi/9) - cos(2*pi/9))))*(x - (i*sin(2*pi/9) - cos(2*pi/9))))*(x - (cos(pi/18)/2 - i*sin(pi/18)/2 + sqrt(3)*sin(pi/18)/2 - i*sqrt(3)*cos(pi/18)/2)))*(x - (cos(pi/18)/2 - i*sin(pi/18)/2 - sqrt(3)*sin(pi/18)/2 + i*sqrt(3)*cos(pi/18)/2)))*(x + (cos(2*pi/9)/2 + i*sin(2*pi/9)/2 + sqrt(3)*sin(2*pi/9)/2 - i*sqrt(3)*cos(2*pi/9)/2)))*(x + (cos(2*pi/9)/2 - i*sin(2*pi/9)/2 + sqrt(3)*sin(2*pi/9)/2 + i*sqrt(3)*cos(2*pi/9)/2)))*(x - (cos(pi/9)*cos(pi/18) + sin(pi/9)*sin(pi/18) - i*cos(pi/9)*sin(pi/18) - i*cos(pi/18)*sin(pi/9))))*(x - (cos(pi/9)*cos(pi/18) - sin(pi/9)*sin(pi/18) - i*cos(pi/9)*sin(pi/18) + i*cos(pi/18)*sin(pi/9))))*(x - (cos(pi/18)*cos(2*pi/9) + sin(pi/18)*sin(2*pi/9) - i*cos(pi/18)*sin(2*pi/9) - i*cos(2*pi/9)*sin(pi/18))))*(x - (cos(pi/18)*cos(2*pi/9) - sin(pi/18)*sin(2*pi/9) - i*cos(2*pi/9)*sin(pi/18) + i*cos(pi/18)*sin(2*pi/9))))*(x - (cos(pi/18)*cos(4*pi/9) + sin(pi/18)*sin(4*pi/9) - i*cos(pi/18)*sin(4*pi/9) - i*cos(4*pi/9)*sin(pi/18))))*(x + (cos(pi/9)*cos(pi/18) + sin(pi/9)*sin(pi/18) - i*cos(pi/18)*sin(pi/9) + i*cos(pi/9)*sin(pi/18))))*(x - (sin(pi/9)*sin(pi/18) + cos(pi/9)*cos(pi/18) + i*cos(pi/9)*sin(pi/18) + i*cos(pi/18)*sin(pi/9))))*(x + (cos(pi/18)*cos(2*pi/9) + sin(pi/18)*sin(2*pi/9) - i*cos(pi/18)*sin(2*pi/9) + i*cos(2*pi/9)*sin(pi/18))))*(x - (sin(pi/18)*sin(2*pi/9) + cos(pi/18)*cos(2*pi/9) + i*cos(pi/18)*sin(2*pi/9) + i*cos(2*pi/9)*sin(pi/18))))*(x + (cos(pi/18)*cos(4*pi/9) + sin(pi/18)*sin(4*pi/9) - i*cos(pi/18)*sin(4*pi/9) + i*cos(4*pi/9)*sin(pi/18))))*(x - (sin(pi/18)*sin(4*pi/9) + cos(pi/18)*cos(4*pi/9) + i*cos(pi/18)*sin(4*pi/9) + i*cos(4*pi/9)*sin(pi/18))))*(x - (cos(pi/18)*cos(4*pi/9) - sin(pi/18)*sin(4*pi/9) - i*cos(4*pi/9)*sin(pi/18) + i*cos(pi/18)*sin(4*pi/9))))*(x + (cos(pi/18)/2 + i*sin(pi/18)/2 + sqrt(3)*sin(pi/18)/2 - i*sqrt(3)*cos(pi/18)/2)))*(x + (cos(pi/18)/2 - sqrt(3)*sin(pi/18)/2 + i*sin(pi/18)/2 + i*sqrt(3)*cos(pi/18)/2)))*(x + (cos(pi/9)/2 + i*sin(pi/9)/2 + sqrt(3)*sin(pi/9)/2 - i*sqrt(3)*cos(pi/9)/2)))*(x + (cos(pi/9)/2 - i*sin(pi/9)/2 + sqrt(3)*sin(pi/9)/2 + i*sqrt(3)*cos(pi/9)/2)))*(x + (cos(pi/9)/2 - i*sin(pi/9)/2 - sqrt(3)*sin(pi/9)/2 - i*sqrt(3)*cos(pi/9)/2)))*(x + (cos(pi/9)/2 - sqrt(3)*sin(pi/9)/2 + i*sin(pi/9)/2 + i*sqrt(3)*cos(pi/9)/2)))*(x + (cos(2*pi/9)/2 - i*sin(2*pi/9)/2 - sqrt(3)*sin(2*pi/9)/2 - i*sqrt(3)*cos(2*pi/9)/2)))*(x + (cos(2*pi/9)/2 - sqrt(3)*sin(2*pi/9)/2 + i*sin(2*pi/9)/2 + i*sqrt(3)*cos(2*pi/9)/2))
Численный ответ
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x^36*(1.0 + x^3)*(1.0 + x^18)*(-1.0 + x^3)*(1.0 + x^3 + x^6)*(1.0 + x^6 - x^3)
x^36*(1.0 + x^3)*(1.0 + x^18)*(-1.0 + x^3)*(1.0 + x^3 + x^6)*(1.0 + x^6 - x^3)
Степени
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36 / 3\ / 18\ / 3\ / 3 6\ / 6 3\ x *\1 + x /*\1 + x /*\-1 + x /*\1 + x + x /*\1 + x - x /
$$x^{36} \left(x^{3} - 1\right) \left(x^{3} + 1\right) \left(x^{18} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right)$$
x^36*(1 + x^3)*(1 + x^18)*(-1 + x^3)*(1 + x^3 + x^6)*(1 + x^6 - x^3)
Собрать выражение
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36 / 3\ / 18\ / 3\ / 3 6\ / 6 3\ x *\1 + x /*\1 + x /*\-1 + x /*\1 + x + x /*\1 + x - x /
$$x^{36} \left(x^{3} - 1\right) \left(x^{3} + 1\right) \left(x^{18} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right)$$
x^36*(1 + x^3)*(1 + x^18)*(-1 + x^3)*(1 + x^3 + x^6)*(1 + x^6 - x^3)
Объединение рациональных выражений
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36 / 3\ / 18\ / 3\ / 3 6\ / 6 3\ x *\1 + x /*\1 + x /*\-1 + x /*\1 + x + x /*\1 + x - x /
$$x^{36} \left(x^{3} - 1\right) \left(x^{3} + 1\right) \left(x^{18} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right)$$
x^36*(1 + x^3)*(1 + x^18)*(-1 + x^3)*(1 + x^3 + x^6)*(1 + x^6 - x^3)
Рациональный знаменатель
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72 36 x - x
$$x^{72} - x^{36}$$
36 / 3\ / 18\ / 3\ / 3 6\ / 6 3\ x *\1 + x /*\1 + x /*\-1 + x /*\1 + x + x /*\1 + x - x /
$$x^{36} \left(x^{3} - 1\right) \left(x^{3} + 1\right) \left(x^{18} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right)$$
x^36*(1 + x^3)*(1 + x^18)*(-1 + x^3)*(1 + x^3 + x^6)*(1 + x^6 - x^3)
Комбинаторика
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36 / 2\ / 2\ / 2 \ / 3 6\ / 4 2\ / 6 3\ / 12 6\ x *(1 + x)*\1 + x /*(-1 + x)*\1 + x + x /*\1 + x - x/*\1 + x + x /*\1 + x - x /*\1 + x - x /*\1 + x - x /
$$x^{36} \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right) \left(x^{4} - x^{2} + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right) \left(x^{12} - x^{6} + 1\right)$$
x^36*(1 + x)*(1 + x^2)*(-1 + x)*(1 + x + x^2)*(1 + x^2 - x)*(1 + x^3 + x^6)*(1 + x^4 - x^2)*(1 + x^6 - x^3)*(1 + x^12 - x^6)