"Foil" is a way that people remember the 'formula' for multiplying binomials. (An alternative approach is to use "a href="/properties/double-distributive-property.php">double distributive").
FOIL stands for first, outer, inner and last pairs. You are supposed to multiply these pairs as shown below!
Add up each term!
| $$ x^2 $$ |
| $$9x$$ |
| $$7x$$ |
| $$+ 63$$ |
| $$ x^2 + 16x + 63 $$ |
The area of each part of the rectangle can be seen as a 'part' of the FOIL formula.
Let's multiply the following binomials: (X + 3)(X + 2).
First: x • x = $$ x^2 $$
Outer: x • 2 = 2x
Inner: 3 • x = 3x
Last: 3 • 2 = 6
This is like example 1.
First: k • k = k²
Outer: k • -4 = -4k
Inner: 7 • k = 7k
Last: 7 • -4 = -28
Simplify by adding the terms.
| $$ k^2 $$ |
| -4k |
| 7k |
| + (-28) |
| k2+ 3k - 28 |
This is like example 1.
Multiply the first, outer, inner and last pairs.
First: k • k = k²
Outer: k • -5 = -5k
Inner: -3 • k = -3k
Last: -3 • -5 = 15
Simplify by adding the terms.
| k² |
| -5k |
| -3k |
| + 15 |
| k2 − 8k + 15 |
This is like example 1. with the slight twist that you now have to deal with coefficients in from of the variable of each binomial.
Multiply the first, outer, inner and last pairs.
First: 2k • 3k = 6k²
Outer: 2k • -4 = -8k
Inner: 9 • 3 k = 27k
Last: 9 • -4 = -36
Simplify by adding the terms.
| 6k² |
| -8k |
| 27k |
| + (-36) |
| 6k2+ 19k + -36 |
This is like example 1 with the slight twist that you now have to deal with coefficients in form of the variable of each binomial.
Multiply the first, outer, inner and last pairs.
First: 5k • 2k = 10k²
Outer: 5k • 3 = 15k
Inner: -1 • 2k = -2k
Last: -1 • 3 = -3
Simplify by adding the terms.
| 10k² |
| 15k |
| -2k |
| + (-3) |
| 10k2+ 13k + -3 |
