Algebra Period 3 (Tuesday)

CHAPTER 1-5: FACTORING (part 2 starting on p. 25)
First, I'll review what Like Terms are and clear up the difference between
"combining" vs multiplying/dividing terms
LIKE TERMS:
1. Same variable
2. Same exponent
Constants are like terms because they all have no variables
(you can actually say that they have a variable raised to the 0 power,
which is 1 times the coefficient)
Example: 3x + 4 can be thought of as 3x + 4x0.= 3x + 4(1).
You can only combine (add or subtract) like terms.

BUT YOU CAN MULTIPLY/DIVIDE UNLIKE TERMS!
3a(7y) = 21ay
BUT
3a + 7y cannot be simplified

48xy/6x = 8y
BUT
48xy - 6x cannot be simplified

FACTORING
THE MAJOR "WATERSHED" MOMENT IN ALGEBRA I!
Undoing the Distributive Property
5 ( 6y + 11 )
This simplifies to 30y + 55

Now you can WORK BACKWARDS to the way the expression began before you used the distributive property.
In 7th grade, we called this using the distributive property backwards.
Now, in Algebra, we call this FACTORING.
FACTORING IS A KEY CONCEPT TO UNDERSTAND IN ALGEBRA.
WITHOUT IT, YOU WILL STRUGGLE THE ENTIRE YEAR!

Let's use the same problem as above and work backwards (FACTOR)
EXAMPLE: FACTOR 30y + 55

THINK: What do 30y and 55 have in common (What is their GCF?)
They both divide by 5

FACTOR out the GCF of 5
(factoring out is really dividing each term by the 5)

MIDDLE STEP TO UNDERSTAND FACTORING:
5 ( 30y + 55 )
5 5
we haven't changed the value because we've divided each piece by 5 and multiplied by 5 as well
(multiply a number by 5 and then divide it by 5 and you'll see have your starting number!)

FINAL FACTORED FORM: 5 ( 6y + 11 )
Wait a minute...Isn't that what I started with before I used the Distributive Property????
Of course it is! This is the key concept in factoring!!!!!

FACTORING DOES NOT CHANGE THE VALUE OF WHAT YOU STARTED WITH!
It's incognito the same thing!
Therefore, you can always check your factored form by multiplying back to the original simplified form.
If it doesn't get back to that,
YOU HAVEN'T FACTORED PROPERLY!

We say that the factored form and simplified form are EQUIVALENT EXPRESSIONS..
(I say they are INCOGNITO the same thing!)