## Precalculus: Mathematics for Calculus, 7th Edition

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