Quadratic Expansion − Foil Method
(x − 4)(x + 5) can be multiplied out to a quadratic expansion using the foil method.
Foil Method − stands for First, Outer, Inner and Last
Example 1. Expand (x − 4)(x + 5)
Example 2. Expand (x − 4)(3x + 5)
| First | ( | x | )( | x | ) = | + x2 | ||
| Outer | ( | x | )( | + 5 | ) = | + 5x | ||
| Inner | ( | − 4 | )( | x | ) = | −4x | ||
| Last | ( | − 4 | )( | + 5 | ) = | −20 |
= x2 + 5x − 4x − 20
= x2 + x − 20
| First | ( | x | )( | 3x | ) = | + 3x2 | ||
| Outer | ( | x | )( | + 5 | ) = | + 5x | ||
| Inner | ( | − 4 | )( | 3x | ) = | −12x | ||
| Last | ( | − 4 | )( | + 5 | ) = | −20 |
= 3x2 + 5x − 12x − 20
= 3x2 − 7x − 20
Note: 'Expand', 'Multiply out' and 'Remove the brackets' is the same thing
to: 
