Господин Экзамен

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Раскрыть скобки в (x^18-10*x^17+43*x^16-102*x^15+141*x^14-108*x^13+36*x^12+2*x^9-10*x^8+18*x^7-12*x^6+1)*(1+x^19-16*x^18+118*x^17-528*x^16+1587*x^15-3348*x^14+5022*x^13-5292*x*12+3753*x^11-1619*x^10+317*x^9+19*x^8-21*x^7-3*x^6+27*x^5-18*x^4)

Выражение, которое надо упростить:

Решение

Вы ввели [src]
/ 18       17       16        15        14        13       12      9       8       7       6    \ /     19       18        17        16         15         14         13                     11         10        9       8       7      6       5       4\
\x   - 10*x   + 43*x   - 102*x   + 141*x   - 108*x   + 36*x   + 2*x  - 10*x  + 18*x  - 12*x  + 1/*\1 + x   - 16*x   + 118*x   - 528*x   + 1587*x   - 3348*x   + 5022*x   - 5292*x*12 + 3753*x   - 1619*x   + 317*x  + 19*x  - 21*x  - 3*x  + 27*x  - 18*x /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 5292 x 12 + 1\right)$$
(x^18 - 10*x^17 + 43*x^16 - 102*x^15 + 141*x^14 - 108*x^13 + 36*x^12 + 2*x^9 - 10*x^8 + 18*x^7 - 12*x^6 + 1)*(1 + x^19 - 16*x^18 + 118*x^17 - 528*x^16 + 1587*x^15 - 3348*x^14 + 5022*x^13 - 5292*x*12 + 3753*x^11 - 1619*x^10 + 317*x^9 + 19*x^8 - 21*x^7 - 3*x^6 + 27*x^5 - 18*x^4)
Общее упрощение [src]
/     18        13        15       6       8       17      9       7       12       16        14\ /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
\1 + x   - 108*x   - 102*x   - 12*x  - 10*x  - 10*x   + 2*x  + 18*x  + 36*x   + 43*x   + 141*x  /*\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
(1 + x^18 - 108*x^13 - 102*x^15 - 12*x^6 - 10*x^8 - 10*x^17 + 2*x^9 + 18*x^7 + 36*x^12 + 43*x^16 + 141*x^14)*(1 + x^19 - 63504*x - 3348*x^14 - 1619*x^10 - 528*x^16 - 21*x^7 - 18*x^4 - 16*x^18 - 3*x^6 + 19*x^8 + 27*x^5 + 118*x^17 + 317*x^9 + 1587*x^15 + 3753*x^11 + 5022*x^13)
Объединение рациональных выражений [src]
/     18        13        15       6       8       17      9       7       12       16        14\ /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
\1 + x   - 108*x   - 102*x   - 12*x  - 10*x  - 10*x   + 2*x  + 18*x  + 36*x   + 43*x   + 141*x  /*\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
(1 + x^18 - 108*x^13 - 102*x^15 - 12*x^6 - 10*x^8 - 10*x^17 + 2*x^9 + 18*x^7 + 36*x^12 + 43*x^16 + 141*x^14)*(1 + x^19 - 63504*x - 3348*x^14 - 1619*x^10 - 528*x^16 - 21*x^7 - 18*x^4 - 16*x^18 - 3*x^6 + 19*x^8 + 27*x^5 + 118*x^17 + 317*x^9 + 1587*x^15 + 3753*x^11 + 5022*x^13)
Степени [src]
/     18        13        15       6       8       17      9       7       12       16        14\ /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
\1 + x   - 108*x   - 102*x   - 12*x  - 10*x  - 10*x   + 2*x  + 18*x  + 36*x   + 43*x   + 141*x  /*\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
(1 + x^18 - 108*x^13 - 102*x^15 - 12*x^6 - 10*x^8 - 10*x^17 + 2*x^9 + 18*x^7 + 36*x^12 + 43*x^16 + 141*x^14)*(1 + x^19 - 63504*x - 3348*x^14 - 1619*x^10 - 528*x^16 - 21*x^7 - 18*x^4 - 16*x^18 - 3*x^6 + 19*x^8 + 27*x^5 + 118*x^17 + 317*x^9 + 1587*x^15 + 3753*x^11 + 5022*x^13)
Комбинаторика [src]
                                                         2                                                                                                                                                        
        2 /      8        2    3    4    5      7      6\  /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
(-1 + x) *\-1 + x  - x - x  - x  - x  - x  - 4*x  + 5*x / *\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x - 1\right)^{2} \left(x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1\right)^{2} \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
(-1 + x)^2*(-1 + x^8 - x - x^2 - x^3 - x^4 - x^5 - 4*x^7 + 5*x^6)^2*(1 + x^19 - 63504*x - 3348*x^14 - 1619*x^10 - 528*x^16 - 21*x^7 - 18*x^4 - 16*x^18 - 3*x^6 + 19*x^8 + 27*x^5 + 118*x^17 + 317*x^9 + 1587*x^15 + 3753*x^11 + 5022*x^13)
Собрать выражение [src]
/     18        13        15       6       8       17      9       7       12       16        14\ /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
\1 + x   - 108*x   - 102*x   - 12*x  - 10*x  - 10*x   + 2*x  + 18*x  + 36*x   + 43*x   + 141*x  /*\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
(1 + x^18 - 108*x^13 - 102*x^15 - 12*x^6 - 10*x^8 - 10*x^17 + 2*x^9 + 18*x^7 + 36*x^12 + 43*x^16 + 141*x^14)*(1 + x^19 - 63504*x - 3348*x^14 - 1619*x^10 - 528*x^16 - 21*x^7 - 18*x^4 - 16*x^18 - 3*x^6 + 19*x^8 + 27*x^5 + 118*x^17 + 317*x^9 + 1587*x^15 + 3753*x^11 + 5022*x^13)
Численный ответ [src]
(1.0 + x^18 + 2.0*x^9 + 18.0*x^7 + 36.0*x^12 + 43.0*x^16 + 141.0*x^14 - 12.0*x^6 - 10.0*x^8 - 10.0*x^17 - 108.0*x^13 - 102.0*x^15)*(1.0 + x^19 + 19.0*x^8 + 27.0*x^5 + 118.0*x^17 + 317.0*x^9 + 1587.0*x^15 + 5022.0*x^13 + 3753.0*x^11 - 16.0*x^18 - 3.0*x^6 - 18.0*x^4 - 21.0*x^7 - 528.0*x^16 - 3348.0*x^14 - 1619.0*x^10 - 63504.0*x)
(1.0 + x^18 + 2.0*x^9 + 18.0*x^7 + 36.0*x^12 + 43.0*x^16 + 141.0*x^14 - 12.0*x^6 - 10.0*x^8 - 10.0*x^17 - 108.0*x^13 - 102.0*x^15)*(1.0 + x^19 + 19.0*x^8 + 27.0*x^5 + 118.0*x^17 + 317.0*x^9 + 1587.0*x^15 + 5022.0*x^13 + 3753.0*x^11 - 16.0*x^18 - 3.0*x^6 - 18.0*x^4 - 21.0*x^7 - 528.0*x^16 - 3348.0*x^14 - 1619.0*x^10 - 63504.0*x)
Рациональный знаменатель [src]
/     18        13        15       6       8       17      9       7       12       16        14\ /     19                   14         10        16       7       4       18      6       8       5        17        9         15         11         13\
\1 + x   - 108*x   - 102*x   - 12*x  - 10*x  - 10*x   + 2*x  + 18*x  + 36*x   + 43*x   + 141*x  /*\1 + x   - 63504*x - 3348*x   - 1619*x   - 528*x   - 21*x  - 18*x  - 16*x   - 3*x  + 19*x  + 27*x  + 118*x   + 317*x  + 1587*x   + 3753*x   + 5022*x  /
$$\left(x^{18} - 10 x^{17} + 43 x^{16} - 102 x^{15} + 141 x^{14} - 108 x^{13} + 36 x^{12} + 2 x^{9} - 10 x^{8} + 18 x^{7} - 12 x^{6} + 1\right) \left(x^{19} - 16 x^{18} + 118 x^{17} - 528 x^{16} + 1587 x^{15} - 3348 x^{14} + 5022 x^{13} + 3753 x^{11} - 1619 x^{10} + 317 x^{9} + 19 x^{8} - 21 x^{7} - 3 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1\right)$$
     37            15            17            13            28            8            26           24           30           19           10           21                    32         22         34       36       4       6       5        35        12         11          33           20           31           23           9           18           7           29           25            27            16            14
1 + x   - 8955837*x   - 2804958*x   - 2281338*x   - 1213863*x   - 1143063*x  - 1118064*x   - 654143*x   - 443826*x   - 159324*x   - 128411*x   - 121482*x   - 63504*x - 56322*x   - 9690*x   - 2498*x   - 26*x   - 18*x  - 15*x  + 27*x  + 321*x   + 738*x   + 3105*x   + 13714*x   + 137079*x   + 179001*x   + 318387*x   + 635359*x  + 713841*x   + 762045*x  + 846234*x   + 885987*x   + 1304662*x   + 6501177*x   + 6854703*x  
$$x^{37} - 26 x^{36} + 321 x^{35} - 2498 x^{34} + 13714 x^{33} - 56322 x^{32} + 179001 x^{31} - 443826 x^{30} + 846234 x^{29} - 1213863 x^{28} + 1304662 x^{27} - 1118064 x^{26} + 885987 x^{25} - 654143 x^{24} + 318387 x^{23} - 9690 x^{22} - 121482 x^{21} + 137079 x^{20} - 159324 x^{19} + 713841 x^{18} - 2804958 x^{17} + 6501177 x^{16} - 8955837 x^{15} + 6854703 x^{14} - 2281338 x^{13} + 738 x^{12} + 3105 x^{11} - 128411 x^{10} + 635359 x^{9} - 1143063 x^{8} + 762045 x^{7} - 15 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1$$
1 + x^37 - 8955837*x^15 - 2804958*x^17 - 2281338*x^13 - 1213863*x^28 - 1143063*x^8 - 1118064*x^26 - 654143*x^24 - 443826*x^30 - 159324*x^19 - 128411*x^10 - 121482*x^21 - 63504*x - 56322*x^32 - 9690*x^22 - 2498*x^34 - 26*x^36 - 18*x^4 - 15*x^6 + 27*x^5 + 321*x^35 + 738*x^12 + 3105*x^11 + 13714*x^33 + 137079*x^20 + 179001*x^31 + 318387*x^23 + 635359*x^9 + 713841*x^18 + 762045*x^7 + 846234*x^29 + 885987*x^25 + 1304662*x^27 + 6501177*x^16 + 6854703*x^14
Общий знаменатель [src]
     37            15            17            13            28            8            26           24           30           19           10           21                    32         22         34       36       4       6       5        35        12         11          33           20           31           23           9           18           7           29           25            27            16            14
1 + x   - 8955837*x   - 2804958*x   - 2281338*x   - 1213863*x   - 1143063*x  - 1118064*x   - 654143*x   - 443826*x   - 159324*x   - 128411*x   - 121482*x   - 63504*x - 56322*x   - 9690*x   - 2498*x   - 26*x   - 18*x  - 15*x  + 27*x  + 321*x   + 738*x   + 3105*x   + 13714*x   + 137079*x   + 179001*x   + 318387*x   + 635359*x  + 713841*x   + 762045*x  + 846234*x   + 885987*x   + 1304662*x   + 6501177*x   + 6854703*x  
$$x^{37} - 26 x^{36} + 321 x^{35} - 2498 x^{34} + 13714 x^{33} - 56322 x^{32} + 179001 x^{31} - 443826 x^{30} + 846234 x^{29} - 1213863 x^{28} + 1304662 x^{27} - 1118064 x^{26} + 885987 x^{25} - 654143 x^{24} + 318387 x^{23} - 9690 x^{22} - 121482 x^{21} + 137079 x^{20} - 159324 x^{19} + 713841 x^{18} - 2804958 x^{17} + 6501177 x^{16} - 8955837 x^{15} + 6854703 x^{14} - 2281338 x^{13} + 738 x^{12} + 3105 x^{11} - 128411 x^{10} + 635359 x^{9} - 1143063 x^{8} + 762045 x^{7} - 15 x^{6} + 27 x^{5} - 18 x^{4} - 63504 x + 1$$
1 + x^37 - 8955837*x^15 - 2804958*x^17 - 2281338*x^13 - 1213863*x^28 - 1143063*x^8 - 1118064*x^26 - 654143*x^24 - 443826*x^30 - 159324*x^19 - 128411*x^10 - 121482*x^21 - 63504*x - 56322*x^32 - 9690*x^22 - 2498*x^34 - 26*x^36 - 18*x^4 - 15*x^6 + 27*x^5 + 321*x^35 + 738*x^12 + 3105*x^11 + 13714*x^33 + 137079*x^20 + 179001*x^31 + 318387*x^23 + 635359*x^9 + 713841*x^18 + 762045*x^7 + 846234*x^29 + 885987*x^25 + 1304662*x^27 + 6501177*x^16 + 6854703*x^14