Question

Use FOIL to explain how to find the product of (a + b)(a − b). Then describe a shortcut that you could use to get this product without using FOIL.

Answer 1

Multiply the first, outside, inside, and last terms of the binomials.

Multiply a times a, a times -b, b times a, and b times -b.

This is the same as just squaring a and squaring b.

A shortcut is to add a squared and b squared.

Answer 2

Greetings!

FOIL stands for:

Front
Outside
Inside
Last

This tells which terms to multiply when using the Distributive Property.
(NOTE: Only applicable with 2-term Polynomials)

For Example:

`(a+b)(a-b)`

Multiply the Fronts of both Equations:

`(a*a)`

Multiply the Outsides of both Equations:

`(a*a)+(a*-b)`

Multiply the Insides of both Equations:

`(a*a)+(a*-b)+(b*a)`

Multiply the Lasts of both Equations:

`(a*a)+(a*-b)+(b*a)+(b*-b)`

Simplify.

`=a^2-ab+ba-b^2`


`=a^2-b^2`


Alternative Method (My Prefered Method)

`(a+b)(a-b)=a(a+b)-b(a+b)`

Use Regular Distributive Property.

`a(a+b)-b(a+b)`


`a*a+a*b-b*a+-b*b`

Simplify.

`a^2+ab-ba+-b^2`


`a^2-b^2`

Hope this helps.
-Benjamin