Algebra ( Period 5)

Special Products 8-4

Learning to recognize some special products- it makes multiplying easier

Remember: you can FOIL these just like the other products until you remember these special patterns  but when we get to factoring  it really helps 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 very happy !!

Difference of Two squares

You will notice that the two factors are Identical except that they have different signs
(x + 6)(x – 6) = x² – 6x + 6x – 36 = x²  – 36  The middle terms drop out.

This will happen EVERY TIME
The middle terms are additive inverses so they become ZERO
You are 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) + 36=  x²+ 12x + 36

If you had foiled it
x²+ 6x + 6x + 36 à can you see that the 2 middle terms are just doubling up?

Another Example
(x - 6)² = ( x - 6)(x - 6) = x² -2(6x) + 36=  x² - 12x + 36

PLEASE NOTE:  Noticing these special products helps you do these multiplication FASTER
If you ever forget them, just FOIL ( or box)
You will need to start recognizing them for factoring!!