# How do you FOIL (x-2)(x+3)?

May 28, 2015

FOIL stands for "First, Outer, Inner, Last."

• "First" refers to the first term of each factor: here, this would be $x$ and $x$
• "Outer" refers to the outermost terms of each factor: here this would be $x$ and $3$
• "Inner" refers to the innermost terms of each factor (those nearest the middle): here this would be $- 2$ and $x$
• "Last" refers to the last term of each factor: here this would be $- 2$ and $3$

Utilizing the foil method, one adds together the indicated products (so the product of the First terms, plus the product of the Outer terms, etc.)

F: $x \cdot x = {x}^{2}$
O: $x \cdot 3 = 3 x$
I: $- 2 \cdot x = - 2 x$
L: $- 2 \cdot 3 = - 6$

Adding these together yields

${x}^{2} + 3 x - 2 x - 6 = {x}^{2} + x - 6$