Раскрыть скобки в (1-v)*((1-u)*(x*a+y*b)+u* ... b*y)+(1-u)*(a*a*x+b*a*y))

Вы ввели

(1 - v)*((1 - u)*(x*a + y*b) + u*((x - 1)*c + y*d)) + v*((1 - u)*(x*f + (y - 1)*g) + u*((x - 1)*h + (y - 1)*k))*v*(u*(a*(b + 1)*(x - 1) + b*(b + 1)*(y - 1)) + (1 - u)*(a*(a + 1)*x + b*(a + 1)*(y - 1))) + (1 - v)*(u*(a*b*(x - 1) + b*b*y) + (1 - u)*(a*a*x + b*a*y))

$$\left(1 - v\right) \left(u \left(y b b + a b \left(x - 1\right)\right) + \left(1 - u\right) \left(x a a + y a b\right)\right) + \left(v v \left(u \left(h \left(x - 1\right) + k \left(y - 1\right)\right) + \left(1 - u\right) \left(f x + g \left(y - 1\right)\right)\right) \left(u \left(a \left(b + 1\right) \left(x - 1\right) + b \left(b + 1\right) \left(y - 1\right)\right) + \left(1 - u\right) \left(x a \left(a + 1\right) + b \left(a + 1\right) \left(y - 1\right)\right)\right) + \left(1 - v\right) \left(u \left(c \left(x - 1\right) + d y\right) + \left(1 - u\right) \left(a x + b y\right)\right)\right)$$

Степени

                                                               /  /   2               \           /   2        \\    2                                                                                                                                                      
(1 - v)*(u*(c*(-1 + x) + d*y) + (1 - u)*(a*x + b*y)) + (1 - v)*\u*\y*b  + a*b*(-1 + x)/ + (1 - u)*\x*a  + a*b*y// + v *(u*(h*(-1 + x) + k*(-1 + y)) + (1 - u)*(f*x + g*(-1 + y)))*(u*(a*(1 + b)*(-1 + x) + b*(1 + b)*(-1 + y)) + (1 - u)*(a*x*(1 + a) + b*(1 + a)*(-1 + y)))

$$v^{2} \left(u \left(h \left(x - 1\right) + k \left(y - 1\right)\right) + \left(1 - u\right) \left(f x + g \left(y - 1\right)\right)\right) \left(u \left(a \left(b + 1\right) \left(x - 1\right) + b \left(b + 1\right) \left(y - 1\right)\right) + \left(1 - u\right) \left(a x \left(a + 1\right) + b \left(a + 1\right) \left(y - 1\right)\right)\right) + \left(1 - v\right) \left(u \left(c \left(x - 1\right) + d y\right) + \left(1 - u\right) \left(a x + b y\right)\right) + \left(1 - v\right) \left(u \left(a b \left(x - 1\right) + b^{2} y\right) + \left(1 - u\right) \left(a^{2} x + a b y\right)\right)$$

Численный ответ

(1.0 - v)*(u*(c*(-1.0 + x) + d*y) + (1.0 - u)*(a*x + b*y)) + (1.0 - v)*(u*(y*b^2 + a*b*(-1.0 + x)) + (1.0 - u)*(x*a^2 + a*b*y)) + v^2*(u*(h*(-1.0 + x) + k*(-1.0 + y)) + (1.0 - u)*(f*x + g*(-1.0 + y)))*(u*(a*(1.0 + b)*(-1.0 + x) + b*(1.0 + b)*(-1.0 + y)) + (1.0 - u)*(a*x*(1.0 + a) + b*(1.0 + a)*(-1.0 + y)))

Рациональный знаменатель

                                                               /  /   2               \           /   2        \\    2                                                                                                                                                      
(1 - v)*(u*(c*(-1 + x) + d*y) + (1 - u)*(a*x + b*y)) + (1 - v)*\u*\y*b  + a*b*(-1 + x)/ + (1 - u)*\x*a  + a*b*y// + v *(u*(h*(-1 + x) + k*(-1 + y)) + (1 - u)*(f*x + g*(-1 + y)))*(u*(a*(1 + b)*(-1 + x) + b*(1 + b)*(-1 + y)) + (1 - u)*(a*x*(1 + a) + b*(1 + a)*(-1 + y)))

$$v^{2} \left(u \left(h \left(x - 1\right) + k \left(y - 1\right)\right) + \left(1 - u\right) \left(f x + g \left(y - 1\right)\right)\right) \left(u \left(a \left(b + 1\right) \left(x - 1\right) + b \left(b + 1\right) \left(y - 1\right)\right) + \left(1 - u\right) \left(a x \left(a + 1\right) + b \left(a + 1\right) \left(y - 1\right)\right)\right) + \left(1 - v\right) \left(u \left(c \left(x - 1\right) + d y\right) + \left(1 - u\right) \left(a x + b y\right)\right) + \left(1 - v\right) \left(u \left(a b \left(x - 1\right) + b^{2} y\right) + \left(1 - u\right) \left(a^{2} x + a b y\right)\right)$$

Объединение рациональных выражений

                                                                                                                   2                                                                                                                                      
(1 - v)*(u*(c*(-1 + x) + d*y) + (1 - u)*(a*x + b*y)) + (1 - v)*(a*(1 - u)*(a*x + b*y) + b*u*(a*(-1 + x) + b*y)) + v *(u*(h*(-1 + x) + k*(-1 + y)) + (1 - u)*(f*x + g*(-1 + y)))*(u*(1 + b)*(a*(-1 + x) + b*(-1 + y)) + (1 + a)*(1 - u)*(a*x + b*(-1 + y)))

$$v^{2} \left(u \left(h \left(x - 1\right) + k \left(y - 1\right)\right) + \left(1 - u\right) \left(f x + g \left(y - 1\right)\right)\right) \left(u \left(b + 1\right) \left(a \left(x - 1\right) + b \left(y - 1\right)\right) + \left(1 - u\right) \left(a + 1\right) \left(a x + b \left(y - 1\right)\right)\right) + \left(1 - v\right) \left(u \left(c \left(x - 1\right) + d y\right) + \left(1 - u\right) \left(a x + b y\right)\right) + \left(1 - v\right) \left(a \left(1 - u\right) \left(a x + b y\right) + b u \left(a \left(x - 1\right) + b y\right)\right)$$

Общее упрощение

                                                                                                                       2                                                                                                                                        
(-1 + v)*(a*(-1 + u)*(a*x + b*y) - b*u*(a*(-1 + x) + b*y)) - (-1 + v)*(u*(c*(-1 + x) + d*y) - (-1 + u)*(a*x + b*y)) + v *(u*(h*(-1 + x) + k*(-1 + y)) - (-1 + u)*(f*x + g*(-1 + y)))*(u*(1 + b)*(a*(-1 + x) + b*(-1 + y)) - (1 + a)*(-1 + u)*(a*x + b*(-1 + y)))

$$v^{2} \left(u \left(h \left(x - 1\right) + k \left(y - 1\right)\right) - \left(u - 1\right) \left(f x + g \left(y - 1\right)\right)\right) \left(u \left(b + 1\right) \left(a \left(x - 1\right) + b \left(y - 1\right)\right) - \left(a + 1\right) \left(u - 1\right) \left(a x + b \left(y - 1\right)\right)\right) - \left(v - 1\right) \left(u \left(c \left(x - 1\right) + d y\right) - \left(u - 1\right) \left(a x + b y\right)\right) + \left(v - 1\right) \left(a \left(u - 1\right) \left(a x + b y\right) - b u \left(a \left(x - 1\right) + b y\right)\right)$$

Общий знаменатель

               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          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        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            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          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  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                2              2  2                2              2  2                2                2              2  2              2  2              2  2                  2
a*x + b*y + x*a  - c*u + a*b*y + b*g*v  + c*u*v + c*u*x + d*u*y + u*y*b  - a*b*u - a*u*x - a*v*x - b*u*y - b*v*y - u*x*a  - v*x*a  + a*b*g*v  + a*b*u*v + a*b*u*x + a*f*v *x  + a*g*u*v  + a*h*u *v  + a*k*u *v  + a*u*v*x + b*g*v *y  + b*h*u*v  + b*k*u*v  + b*u*v*y + f*a *v *x  + g*u*b *v  + h*b *u *v  + k*b *u *v  + u*v*x*a  - a*b*u*y - a*b*v*y - a*g*x*v  - a*g*u *v  - b*f*x*v  - b*g*u*v  - c*u*v*x - d*u*v*y - g*x*a *v  - g*b *u *v  - u*v*y*b  - 2*b*g*y*v  + a*b*g*v *y  + a*b*h*u*v  + a*b*k*u*v  + a*b*u*v*y + a*f*x*u *v  + a*g*u*x*v  + a*g*x*y*v  + a*g*y*u *v  + a*h*u*v *x  + b*f*u*x*v  + b*f*x*y*v  + b*k*u*v *y  + f*x*b *u *v  + f*a *u *v *x  + g*u*b *v *y  + g*x*y*a *v  + h*u*a *v *x  + h*x*a *u *v  + k*x*a *u *v  + k*b *u *v *y  - a*b*f*x*v  - a*b*g*u*v  - a*b*u*v*x - a*f*u*x*v  - a*f*u*v *x  - a*g*u*y*v  - a*h*u*x*v  - a*h*x*u *v  - a*k*u*x*v  - a*k*y*u *v  - b*g*u*v *y  - b*h*u*x*v  - b*h*u*y*v  - f*u*x*b *v  - g*x*a *u *v  - g*b *u *v *y  - h*u*x*a *v  - h*x*b *u *v  - h*y*b *u *v  - h*a *u *v *x  - k*u*x*a *v  - 2*a*b*g*y*v  - 2*b*k*u*y*v  - 2*f*u*a *v *x  - 2*g*u*y*b *v  - 2*k*y*b *u *v  + 2*b*g*u*y*v  + 2*g*u*x*a *v  + 2*g*y*b *u *v  + a*b*f*u*x*v  + a*b*f*u*v *x  + a*b*f*x*y*v  + a*b*g*x*u *v  + a*b*g*u *v *y  + a*b*h*y*u *v  + a*b*h*u *v *x  + a*b*k*u*v *y  + a*b*k*y*u *v  + a*k*u*x*y*v  + b*h*u*x*y*v  + f*u*x*y*b *v  + g*x*y*a *u *v  + h*x*y*b *u *v  + k*u*x*y*a *v  - a*b*f*u *v *x  - a*b*g*u*x*v  - a*b*g*y*u *v  - a*b*h*u*x*v  - a*b*h*u*y*v  - a*b*h*x*u *v  - a*b*k*x*u *v  - a*b*k*u *v *y  - a*g*u*x*y*v  - b*f*u*x*y*v  - f*x*y*b *u *v  - k*x*y*a *u *v  - 2*a*b*g*u*v *y  - 2*a*b*k*u*y*v  - 2*g*u*x*y*a *v  + 3*a*b*g*u*y*v  + a*b*f*x*y*u *v  + a*b*g*u*x*y*v  + a*b*h*u*x*y*v  + a*b*k*x*y*u *v  - a*b*g*x*y*u *v  - a*b*h*x*y*u *v  - 2*a*b*f*u*x*y*v 

$$a^{2} f u^{2} v^{2} x^{2} - 2 a^{2} f u v^{2} x^{2} + a^{2} f v^{2} x^{2} + a^{2} g u^{2} v^{2} x y - a^{2} g u^{2} v^{2} x - 2 a^{2} g u v^{2} x y + 2 a^{2} g u v^{2} x + a^{2} g v^{2} x y - a^{2} g v^{2} x - a^{2} h u^{2} v^{2} x^{2} + a^{2} h u^{2} v^{2} x + a^{2} h u v^{2} x^{2} - a^{2} h u v^{2} x - a^{2} k u^{2} v^{2} x y + a^{2} k u^{2} v^{2} x + a^{2} k u v^{2} x y - a^{2} k u v^{2} x + a^{2} u v x - a^{2} u x - a^{2} v x + a^{2} x - a b f u^{2} v^{2} x^{2} + a b f u^{2} v^{2} x y + a b f u v^{2} x^{2} - 2 a b f u v^{2} x y + a b f u v^{2} x + a b f v^{2} x y - a b f v^{2} x - a b g u^{2} v^{2} x y + a b g u^{2} v^{2} x + a b g u^{2} v^{2} y^{2} - a b g u^{2} v^{2} y + a b g u v^{2} x y - a b g u v^{2} x - 2 a b g u v^{2} y^{2} + 3 a b g u v^{2} y - a b g u v^{2} + a b g v^{2} y^{2} - 2 a b g v^{2} y + a b g v^{2} + a b h u^{2} v^{2} x^{2} - a b h u^{2} v^{2} x y - a b h u^{2} v^{2} x + a b h u^{2} v^{2} y + a b h u v^{2} x y - a b h u v^{2} x - a b h u v^{2} y + a b h u v^{2} + a b k u^{2} v^{2} x y - a b k u^{2} v^{2} x - a b k u^{2} v^{2} y^{2} + a b k u^{2} v^{2} y + a b k u v^{2} y^{2} - 2 a b k u v^{2} y + a b k u v^{2} - a b u v x + a b u v y + a b u v + a b u x - a b u y - a b u - a b v y + a b y + a f u^{2} v^{2} x - a f u v^{2} x^{2} - a f u v^{2} x + a f v^{2} x^{2} + a g u^{2} v^{2} y - a g u^{2} v^{2} - a g u v^{2} x y + a g u v^{2} x - a g u v^{2} y + a g u v^{2} + a g v^{2} x y - a g v^{2} x - a h u^{2} v^{2} x + a h u^{2} v^{2} + a h u v^{2} x^{2} - a h u v^{2} x - a k u^{2} v^{2} y + a k u^{2} v^{2} + a k u v^{2} x y - a k u v^{2} x + a u v x - a u x - a v x + a x - b^{2} f u^{2} v^{2} x y + b^{2} f u^{2} v^{2} x + b^{2} f u v^{2} x y - b^{2} f u v^{2} x - b^{2} g u^{2} v^{2} y^{2} + 2 b^{2} g u^{2} v^{2} y - b^{2} g u^{2} v^{2} + b^{2} g u v^{2} y^{2} - 2 b^{2} g u v^{2} y + b^{2} g u v^{2} + b^{2} h u^{2} v^{2} x y - b^{2} h u^{2} v^{2} x - b^{2} h u^{2} v^{2} y + b^{2} h u^{2} v^{2} + b^{2} k u^{2} v^{2} y^{2} - 2 b^{2} k u^{2} v^{2} y + b^{2} k u^{2} v^{2} - b^{2} u v y + b^{2} u y - b f u v^{2} x y + b f u v^{2} x + b f v^{2} x y - b f v^{2} x - b g u v^{2} y^{2} + 2 b g u v^{2} y - b g u v^{2} + b g v^{2} y^{2} - 2 b g v^{2} y + b g v^{2} + b h u v^{2} x y - b h u v^{2} x - b h u v^{2} y + b h u v^{2} + b k u v^{2} y^{2} - 2 b k u v^{2} y + b k u v^{2} + b u v y - b u y - b v y + b y - c u v x + c u v + c u x - c u - d u v y + d u y$$

Комбинаторика

               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          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        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            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          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  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                2              2  2                2              2  2                2                2              2  2              2  2              2  2                  2
a*x + b*y + x*a  - c*u + a*b*y + b*g*v  + c*u*v + c*u*x + d*u*y + u*y*b  - a*b*u - a*u*x - a*v*x - b*u*y - b*v*y - u*x*a  - v*x*a  + a*b*g*v  + a*b*u*v + a*b*u*x + a*f*v *x  + a*g*u*v  + a*h*u *v  + a*k*u *v  + a*u*v*x + b*g*v *y  + b*h*u*v  + b*k*u*v  + b*u*v*y + f*a *v *x  + g*u*b *v  + h*b *u *v  + k*b *u *v  + u*v*x*a  - a*b*u*y - a*b*v*y - a*g*x*v  - a*g*u *v  - b*f*x*v  - b*g*u*v  - c*u*v*x - d*u*v*y - g*x*a *v  - g*b *u *v  - u*v*y*b  - 2*b*g*y*v  + a*b*g*v *y  + a*b*h*u*v  + a*b*k*u*v  + a*b*u*v*y + a*f*x*u *v  + a*g*u*x*v  + a*g*x*y*v  + a*g*y*u *v  + a*h*u*v *x  + b*f*u*x*v  + b*f*x*y*v  + b*k*u*v *y  + f*x*b *u *v  + f*a *u *v *x  + g*u*b *v *y  + g*x*y*a *v  + h*u*a *v *x  + h*x*a *u *v  + k*x*a *u *v  + k*b *u *v *y  - a*b*f*x*v  - a*b*g*u*v  - a*b*u*v*x - a*f*u*x*v  - a*f*u*v *x  - a*g*u*y*v  - a*h*u*x*v  - a*h*x*u *v  - a*k*u*x*v  - a*k*y*u *v  - b*g*u*v *y  - b*h*u*x*v  - b*h*u*y*v  - f*u*x*b *v  - g*x*a *u *v  - g*b *u *v *y  - h*u*x*a *v  - h*x*b *u *v  - h*y*b *u *v  - h*a *u *v *x  - k*u*x*a *v  - 2*a*b*g*y*v  - 2*b*k*u*y*v  - 2*f*u*a *v *x  - 2*g*u*y*b *v  - 2*k*y*b *u *v  + 2*b*g*u*y*v  + 2*g*u*x*a *v  + 2*g*y*b *u *v  + a*b*f*u*x*v  + a*b*f*u*v *x  + a*b*f*x*y*v  + a*b*g*x*u *v  + a*b*g*u *v *y  + a*b*h*y*u *v  + a*b*h*u *v *x  + a*b*k*u*v *y  + a*b*k*y*u *v  + a*k*u*x*y*v  + b*h*u*x*y*v  + f*u*x*y*b *v  + g*x*y*a *u *v  + h*x*y*b *u *v  + k*u*x*y*a *v  - a*b*f*u *v *x  - a*b*g*u*x*v  - a*b*g*y*u *v  - a*b*h*u*x*v  - a*b*h*u*y*v  - a*b*h*x*u *v  - a*b*k*x*u *v  - a*b*k*u *v *y  - a*g*u*x*y*v  - b*f*u*x*y*v  - f*x*y*b *u *v  - k*x*y*a *u *v  - 2*a*b*g*u*v *y  - 2*a*b*k*u*y*v  - 2*g*u*x*y*a *v  + 3*a*b*g*u*y*v  + a*b*f*x*y*u *v  + a*b*g*u*x*y*v  + a*b*h*u*x*y*v  + a*b*k*x*y*u *v  - a*b*g*x*y*u *v  - a*b*h*x*y*u *v  - 2*a*b*f*u*x*y*v 

$$a^{2} f u^{2} v^{2} x^{2} - 2 a^{2} f u v^{2} x^{2} + a^{2} f v^{2} x^{2} + a^{2} g u^{2} v^{2} x y - a^{2} g u^{2} v^{2} x - 2 a^{2} g u v^{2} x y + 2 a^{2} g u v^{2} x + a^{2} g v^{2} x y - a^{2} g v^{2} x - a^{2} h u^{2} v^{2} x^{2} + a^{2} h u^{2} v^{2} x + a^{2} h u v^{2} x^{2} - a^{2} h u v^{2} x - a^{2} k u^{2} v^{2} x y + a^{2} k u^{2} v^{2} x + a^{2} k u v^{2} x y - a^{2} k u v^{2} x + a^{2} u v x - a^{2} u x - a^{2} v x + a^{2} x - a b f u^{2} v^{2} x^{2} + a b f u^{2} v^{2} x y + a b f u v^{2} x^{2} - 2 a b f u v^{2} x y + a b f u v^{2} x + a b f v^{2} x y - a b f v^{2} x - a b g u^{2} v^{2} x y + a b g u^{2} v^{2} x + a b g u^{2} v^{2} y^{2} - a b g u^{2} v^{2} y + a b g u v^{2} x y - a b g u v^{2} x - 2 a b g u v^{2} y^{2} + 3 a b g u v^{2} y - a b g u v^{2} + a b g v^{2} y^{2} - 2 a b g v^{2} y + a b g v^{2} + a b h u^{2} v^{2} x^{2} - a b h u^{2} v^{2} x y - a b h u^{2} v^{2} x + a b h u^{2} v^{2} y + a b h u v^{2} x y - a b h u v^{2} x - a b h u v^{2} y + a b h u v^{2} + a b k u^{2} v^{2} x y - a b k u^{2} v^{2} x - a b k u^{2} v^{2} y^{2} + a b k u^{2} v^{2} y + a b k u v^{2} y^{2} - 2 a b k u v^{2} y + a b k u v^{2} - a b u v x + a b u v y + a b u v + a b u x - a b u y - a b u - a b v y + a b y + a f u^{2} v^{2} x - a f u v^{2} x^{2} - a f u v^{2} x + a f v^{2} x^{2} + a g u^{2} v^{2} y - a g u^{2} v^{2} - a g u v^{2} x y + a g u v^{2} x - a g u v^{2} y + a g u v^{2} + a g v^{2} x y - a g v^{2} x - a h u^{2} v^{2} x + a h u^{2} v^{2} + a h u v^{2} x^{2} - a h u v^{2} x - a k u^{2} v^{2} y + a k u^{2} v^{2} + a k u v^{2} x y - a k u v^{2} x + a u v x - a u x - a v x + a x - b^{2} f u^{2} v^{2} x y + b^{2} f u^{2} v^{2} x + b^{2} f u v^{2} x y - b^{2} f u v^{2} x - b^{2} g u^{2} v^{2} y^{2} + 2 b^{2} g u^{2} v^{2} y - b^{2} g u^{2} v^{2} + b^{2} g u v^{2} y^{2} - 2 b^{2} g u v^{2} y + b^{2} g u v^{2} + b^{2} h u^{2} v^{2} x y - b^{2} h u^{2} v^{2} x - b^{2} h u^{2} v^{2} y + b^{2} h u^{2} v^{2} + b^{2} k u^{2} v^{2} y^{2} - 2 b^{2} k u^{2} v^{2} y + b^{2} k u^{2} v^{2} - b^{2} u v y + b^{2} u y - b f u v^{2} x y + b f u v^{2} x + b f v^{2} x y - b f v^{2} x - b g u v^{2} y^{2} + 2 b g u v^{2} y - b g u v^{2} + b g v^{2} y^{2} - 2 b g v^{2} y + b g v^{2} + b h u v^{2} x y - b h u v^{2} x - b h u v^{2} y + b h u v^{2} + b k u v^{2} y^{2} - 2 b k u v^{2} y + b k u v^{2} + b u v y - b u y - b v y + b y - c u v x + c u v + c u x - c u - d u v y + d u y$$