How do you FOIL (2x - 5y) ( x + y)?

Jun 5, 2015

Given $\left(2 x - 5 y\right) \left(x + y\right)$ pick out pairs of terms to multiply in the order given by FOIL:

First: $2 x \times x = 2 {x}^{2}$
Outside: $2 x \times y = 2 x y$
Inside: $- 5 y \times x = - 5 y x = - 5 x y$
Last: $- 5 y \times y = - 5 {y}^{2}$

Then add these all together to get:

$2 {x}^{2} + 2 x y - 5 x y - 5 {y}^{2} = 2 {x}^{2} - 3 x y - 5 {y}^{2}$