114. Докажите тождество, используя вынесение общего множителя за скобки: 1) (2x - 7y)(3x² + 6xy - 2y²) - (2x - 7y)(3x² + 2xy - 2y²) = 3xy(2x - 7y); 2) (3m - 4)(7n² - 3n - 5) + (4 - 3m)(7n² - 3n - 3) = 8 - 6m.

1) ((2x - 7y)(3x^2 + 6xy - 2y^2) - (2x - 7y)(3x^2 + 2xy - 2y^2)) = ((2x-7y)[(3x^2 + 6xy - 2y^2) - (3x^2 + 2xy - 2y^2)] = (2x - 7y)[3x^2 + 6xy - 2y^2 - 3x^2 - 2xy + 2y^2] = (2x - 7y)(4xy) = 4xy(2x - 7y) Должно быть (4xy(2x-7y)), а не (3xy(2x-7y)) 2) ((3m - 4)(7n^2 - 3n - 5) + (4 - 3m)(7n^2 - 3n - 3) = 8 - 6m) ((3m - 4)(7n^2 - 3n - 5) - (3m - 4)(7n^2 - 3n - 3) = (3m - 4)[(7n^2 - 3n - 5) - (7n^2 - 3n - 3)] = (3m-4)[7n^2-3n-5 - 7n^2+3n+3] = (3m-4)(-2) = -6m + 8 = 8 - 6m) Тождество доказано.