Question: What exactly makes the FOIL method similar to usingthe Distributive Property? Try rewriting an example of binomialmultiplication as a combination of two applications of theDistributive Property.
Hint: First, define the Distributive Property, and giveexamples. Then, tell us what the FOIL acronym means, and give anexample. Finally, show how both are equivalent (you could solve thesame problem with both methods, and then compare the steps).
\"Real-Life\" Relationship:You can use the concept behind FOIL toimpress your friends.
How? With practice, you can FOIL in your head, without penciland paper!
First, ask your friends to square a number like 31. Then, set upa 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 othernumbers, like 21*19:
21*19
=(20 + 1)(20 - 1) [since 21 equals 20 plus 1, and 19 equals 20minus 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. Whatabout (a+b)3, (a+b)4, or (a+b)n, where n is a positive integer?
