Question

Доведіть тотожність (винесіть спільний множник за дужки):

1) (2х – 7у)(3х2 + 5ху – 2у2) – (2х – 7у)(3х2 + 2ху – 2у2) = 3ху(2х – 7у);

2) (3m – 4)(7n2 – 3n – 5) + (4 – 3m)(7n2 – 3n – 3) = 8 – 6m

Answer 1

$1) \ (2x - 7y)(3x^{2} + 5xy - 2y^{2}) - (2x - 7y)(3x^{2} + 2xy - 2y^{2}) = \\= (2x - 7y)(3x^{2} + 5xy - 2y^{2} - (3x^{2} + 2xy - 2y^{2})) =\\= (2x - 7y)(3x^{2} + 5xy - 2y^{2} - 3x^{2} - 2xy + 2y^{2}) =\\= (2x - 7y)3xy = 3xy(2x - 7y)$

$2) \ (3m - 4)(7n^{2} - 3n - 5) + (4 - 3m)(7n^{2} - 3n - 3) =\\= (3m - 4)(7n^{2} - 3n - 5) - (3m - 4)(7n^{2} - 3n - 3) =\\ =(3m - 4)(7n^{2} - 3n - 5 - (7n^{2} - 3n - 3)) = \\= (3m - 4)(7n^{2} - 3n - 5 - 7n^{2} + 3n+ 3) = (3m - 4)(-2) = 8 - 6m$