## Precalculus: Mathematics for Calculus, 7th Edition

2$x^2$ + 5xy - 3$y^2$
The FOIL method stands for First, Outside, Inside, Last. This means you multiply the first term of each binomial together, in this instance x and 2x, giving 2$x^2$. 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 x and -y, giving -xy. 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 3y and 2x, giving 6xy. Finally you multiply the last terms, 3y and -y, giving -3$y^2$. Now add the terms from these four operations: 2$x^2$ + -xy + 6xy + -3$y^2$ 2$x^2$ + 5xy - 3$y^2$