Which of the following polynomials corresponds to the product of the multivariate polynomials 4x - 3y + 5 and x + 2y - - 3?

If the second polynomial is x + 2y - 3, we multiply

(4x - 3y + 5) (x + 2y - 3)

We distribute each term of the first polynomial (4x - 3y + 5) to every term

of the second polynomial (x + 2y - 3):

(4x - 3y + 5) (x + 2y - 3) = 4x^ 2 + 8xy - 12x

- 3xy - 6y^ 2 + 9y

+ 5x + 10y - 15

Then combine similar terms:

(4x - 3y + 5) (x + 2y - 3) = 4x^ 2 - 6y^ 2 + 5xy - 7x + 19y - 15

If the second polynomial is x + 2y - - 3, we multiply

(4x - 3y + 5) (x + 2y + 3) = 4x^ 2 + 8xy + 12x

- 3xy - 6y^ 2 - 9y

+ 5x + 10y + 15

(4x - 3y + 5) (x + 2y - 3) = 4x^ 2 - 6y^ 2 + 5xy + 17x + y + 15