Algebra (Period 1)

Multiplying Binomials: Special Products 5-10

LEARN TO RECOGNIZE SOME SPECIAL PRODUCTS - IT MAKES IT EASIER!


Remember: You can FOIL these just like the other products until you remember these special patterns....but when we get to factoring next week, it will really help you to know these patterns by heart. 

When you do, you actually don't need to show any work because you do it in your head! 

(That should make a lot of you happy! :)



DIFFERENCE OF TWO SQUARES:

You will notice that the two factors are IDENTICAL except they have DIFFERENT SIGNS

(x + 6)(x - 6) =
x² - 6x + 6x - 36 =
x² - 36


This will happen every time!
 
The middle terms are additive inverses so they become zero.


You're left with a difference (subtraction) of two terms that are squared.



SQUARING A BINOMIAL:

When you multiply one binomial by itself (squaring it), you end up with:

First term squared + twice the product of both terms + last term squared


(x + 6)² =
(x + 6)(x + 6) =
x² + 2(6x) + 6² =
x² + 12x + 36


If you foiled you would have:

x²  + 6x + 6x + 36


CAN YOU SEE THAT THE 2 MIDDLE TERMS ARE JUST DOUBLING UP??? 

WHY???


Another example with subtraction in the middle:

(x - 6)² =
(x - 6)(x - 6) =
x² + 2(-6x) + 6² =
x² - 12x + 36


If you foiled you would have:

x² - 6x - 6x + 36


CAN YOU SEE THAT THE 2 MIDDLE TERMS ARE JUST DOUBLING UP??? 
WHY???



PLEASE NOTE:

NOTICING THESE SPECIAL PRODUCTS HELPS YOU DO THESE 
MULTIPLICATIONS FASTER!

IF YOU EVER FORGET THEM, JUST FOIL!


(but you will need to recognize them for factoring in Chapter 6)