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Здравствуйте! Прошу помощи в следующем вопросе: Найти коэффициенты при a=x^2•y^2•z^4, b=x^2•y•z^3, c=x^4•y^2 в разложении (5•x+4•y+z^2)^6. Я понимаю, что речь о полиномиальной теореме, и 1) a=x2•y2•z4 = (x^2)^1•(y^2)^1• (z^2)^2 2) b=x2•y•z3 = (x^2)^1•(y^1)^1• (z^3)^1 3) c=x4•y2 = (x^2)^2•(y^2)^1• (z^1)^0 Но к сожалению, по материалам лекции не могу понять, как верно прописать степени, чтобы прийти к коэффициенту 6. И вижу, что коэффициент по крайней мере при b будет равен 0. Или я ошибаюсь? Подскажите, пожалуйста
При разложении многочлена чтобы вычислить коэффициенты при нужно из скобок взять множитель из скобок взять множитель ..., из скобок взять множитель Этот коэффициент равен Исходя из этого рассмотрим три заданных случая, приняв, что Случай 1 Цитата: Katerina Shugina
В разложении заданного многочлена не может быть слагаемого потому что невозможно получить множитель Можно, наверное, считать, что искомый коэффициент равен нулю. Случай 3 Цитата: Katerina Shugina
c=x^4•y^2
Тогда и искомый коэффициент равен
5
Большое спасибо, я немного разобралась сама, вы подтвердили мои догадки, теперь все встало на свои места)
Об авторе:
Facta loquuntur.
Форма ответа
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чтобы вычислить коэффициенты при 
нужно из 
скобок взять множитель 
из 
скобок взять множитель 
..., из 
скобок взять множитель 
Этот коэффициент равен 
Исходя из этого рассмотрим три заданных случая, приняв, что 
Katerina Shugina 
и искомый коэффициент равен
потому что невозможно получить множитель 
Можно, наверное, считать, что искомый коэффициент равен нулю.
и искомый коэффициент равен