Question

Question: What exactly makes the FOIL method similar to using the Distributive Property? Try rewriting an example of binomial multiplication as a combination of two applications of the Distributive Property.

Hint: First, define the Distributive Property, and give examples. Then, tell us what the FOIL acronym means, and give an example. Finally, show how both are equivalent (you could solve the same problem with both methods, and then compare the steps).

"Real-Life" Relationship:You can use the concept behind FOIL to impress your friends.

How? With practice, you can FOIL in your head, without pencil and paper!

First, ask your friends to square a number like 31. Then, set up a FOIL in your mind:

312 = 31*31

=(30 + 1)(30 + 1) [since 31 equals 30 plus 1]

=30*30 + 30*1 + 1*30 + 1*1 [FOIL]

=900 + 30 + 30 + 1

=961

After you get some practice with squaring, you can try other numbers, like 21*19:

21*19

=(20 + 1)(20 - 1) [since 21 equals 20 plus 1, and 19 equals 20 minus 1]

=20*20 - 20*1 + 1*20 - 1*1

=400 - 20 + 20 - 1

=399

Challenge: We can use FOIL to get a formula for (a+b)2. What about (a+b)3, (a+b)4, or (a+b)n, where n is a positive integer?

Answer 1