Раскрыть скобки в (1+a*x)*(1+b*x)*(1+c*x)*( ... )*(1+e*x)*(1+f*x)*(1+g*x)

Вы ввели

(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + E*x)*(1 + f*x)*(1 + g*x)

$$\left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(e x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Степени

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Численный ответ

(1.0 + 2.71828182845905*x)*(1.0 + a*x)*(1.0 + b*x)*(1.0 + c*x)*(1.0 + d*x)*(1.0 + f*x)*(1.0 + g*x)

Рациональный знаменатель

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Объединение рациональных выражений

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Общее упрощение

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Собрать выражение

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$

Общий знаменатель

                                                   2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2        2          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          3          3          3            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4            4              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5              5                6                6                6                6                6                6                6                  7
1 + E*x + a*x + b*x + c*x + d*x + f*x + g*x + E*a*x  + E*b*x  + E*c*x  + E*d*x  + E*f*x  + E*g*x  + a*b*x  + a*c*x  + a*d*x  + a*f*x  + a*g*x  + b*c*x  + b*d*x  + b*f*x  + b*g*x  + c*d*x  + c*f*x  + c*g*x  + d*f*x  + d*g*x  + f*g*x  + E*a*b*x  + E*a*c*x  + E*a*d*x  + E*a*f*x  + E*a*g*x  + E*b*c*x  + E*b*d*x  + E*b*f*x  + E*b*g*x  + E*c*d*x  + E*c*f*x  + E*c*g*x  + E*d*f*x  + E*d*g*x  + E*f*g*x  + a*b*c*x  + a*b*d*x  + a*b*f*x  + a*b*g*x  + a*c*d*x  + a*c*f*x  + a*c*g*x  + a*d*f*x  + a*d*g*x  + a*f*g*x  + b*c*d*x  + b*c*f*x  + b*c*g*x  + b*d*f*x  + b*d*g*x  + b*f*g*x  + c*d*f*x  + c*d*g*x  + c*f*g*x  + d*f*g*x  + E*a*b*c*x  + E*a*b*d*x  + E*a*b*f*x  + E*a*b*g*x  + E*a*c*d*x  + E*a*c*f*x  + E*a*c*g*x  + E*a*d*f*x  + E*a*d*g*x  + E*a*f*g*x  + E*b*c*d*x  + E*b*c*f*x  + E*b*c*g*x  + E*b*d*f*x  + E*b*d*g*x  + E*b*f*g*x  + E*c*d*f*x  + E*c*d*g*x  + E*c*f*g*x  + E*d*f*g*x  + a*b*c*d*x  + a*b*c*f*x  + a*b*c*g*x  + a*b*d*f*x  + a*b*d*g*x  + a*b*f*g*x  + a*c*d*f*x  + a*c*d*g*x  + a*c*f*g*x  + a*d*f*g*x  + b*c*d*f*x  + b*c*d*g*x  + b*c*f*g*x  + b*d*f*g*x  + c*d*f*g*x  + E*a*b*c*d*x  + E*a*b*c*f*x  + E*a*b*c*g*x  + E*a*b*d*f*x  + E*a*b*d*g*x  + E*a*b*f*g*x  + E*a*c*d*f*x  + E*a*c*d*g*x  + E*a*c*f*g*x  + E*a*d*f*g*x  + E*b*c*d*f*x  + E*b*c*d*g*x  + E*b*c*f*g*x  + E*b*d*f*g*x  + E*c*d*f*g*x  + a*b*c*d*f*x  + a*b*c*d*g*x  + a*b*c*f*g*x  + a*b*d*f*g*x  + a*c*d*f*g*x  + b*c*d*f*g*x  + E*a*b*c*d*f*x  + E*a*b*c*d*g*x  + E*a*b*c*f*g*x  + E*a*b*d*f*g*x  + E*a*c*d*f*g*x  + E*b*c*d*f*g*x  + a*b*c*d*f*g*x  + E*a*b*c*d*f*g*x 

$$e a b c d f g x^{7} + a b c d f g x^{6} + e a b c d f x^{6} + a b c d f x^{5} + e a b c d g x^{6} + a b c d g x^{5} + e a b c d x^{5} + a b c d x^{4} + e a b c f g x^{6} + a b c f g x^{5} + e a b c f x^{5} + a b c f x^{4} + e a b c g x^{5} + a b c g x^{4} + e a b c x^{4} + a b c x^{3} + e a b d f g x^{6} + a b d f g x^{5} + e a b d f x^{5} + a b d f x^{4} + e a b d g x^{5} + a b d g x^{4} + e a b d x^{4} + a b d x^{3} + e a b f g x^{5} + a b f g x^{4} + e a b f x^{4} + a b f x^{3} + e a b g x^{4} + a b g x^{3} + e a b x^{3} + a b x^{2} + e a c d f g x^{6} + a c d f g x^{5} + e a c d f x^{5} + a c d f x^{4} + e a c d g x^{5} + a c d g x^{4} + e a c d x^{4} + a c d x^{3} + e a c f g x^{5} + a c f g x^{4} + e a c f x^{4} + a c f x^{3} + e a c g x^{4} + a c g x^{3} + e a c x^{3} + a c x^{2} + e a d f g x^{5} + a d f g x^{4} + e a d f x^{4} + a d f x^{3} + e a d g x^{4} + a d g x^{3} + e a d x^{3} + a d x^{2} + e a f g x^{4} + a f g x^{3} + e a f x^{3} + a f x^{2} + e a g x^{3} + a g x^{2} + e a x^{2} + a x + e b c d f g x^{6} + b c d f g x^{5} + e b c d f x^{5} + b c d f x^{4} + e b c d g x^{5} + b c d g x^{4} + e b c d x^{4} + b c d x^{3} + e b c f g x^{5} + b c f g x^{4} + e b c f x^{4} + b c f x^{3} + e b c g x^{4} + b c g x^{3} + e b c x^{3} + b c x^{2} + e b d f g x^{5} + b d f g x^{4} + e b d f x^{4} + b d f x^{3} + e b d g x^{4} + b d g x^{3} + e b d x^{3} + b d x^{2} + e b f g x^{4} + b f g x^{3} + e b f x^{3} + b f x^{2} + e b g x^{3} + b g x^{2} + e b x^{2} + b x + e c d f g x^{5} + c d f g x^{4} + e c d f x^{4} + c d f x^{3} + e c d g x^{4} + c d g x^{3} + e c d x^{3} + c d x^{2} + e c f g x^{4} + c f g x^{3} + e c f x^{3} + c f x^{2} + e c g x^{3} + c g x^{2} + e c x^{2} + c x + e d f g x^{4} + d f g x^{3} + e d f x^{3} + d f x^{2} + e d g x^{3} + d g x^{2} + e d x^{2} + d x + e f g x^{3} + f g x^{2} + e f x^{2} + f x + e g x^{2} + g x + e x + 1$$

Комбинаторика

(1 + E*x)*(1 + a*x)*(1 + b*x)*(1 + c*x)*(1 + d*x)*(1 + f*x)*(1 + g*x)

$$\left(e x + 1\right) \left(a x + 1\right) \left(b x + 1\right) \left(c x + 1\right) \left(d x + 1\right) \left(f x + 1\right) \left(g x + 1\right)$$