Question

Докажите тождество (х-у)^3=x^3-y^3-3xy(x-y) ​

Answer 1

(x - y)³ = (x - y)(x - y)(x - y) = (x² - xy - yx + x²)(x - y) = (x² - 2xy + y²)(x - y) = x³ - 2x²y + y²x - x²y + 2xy² - y³ = x³ - 3x²y + 3xy² - y³ = x³ - y³ - 3x²y + 3xy² = x³ - y³ - 3xy(x - y) чтд