#### Answer

12$x^2$ - 19xy + 5$y^2$

#### Work Step by Step

The FOIL method stands for First, Outside, Inside, Last. This means you multiply the first term of each binomial together, in this instance 4x and 3x, giving 12$x^2$. Next you multiply the two "Outside" terms, meaning the first term of the first expression and the second term of the second expression, in this case 4x and -y, giving -4xy. Next you multiply the "Inside" terms, meaning the second term of the first expression and the first term of the second expression, in this case -5y and 3x, giving -15xy. Finally you multiply the last terms, -5y and -y, giving 5$y^2$. Now add the terms from these four operations:
12$x^2$ + -4xy + -15xy + 5y2
12$x^2$ - 19xy + 5$y^2$