Hello boys and girls.
Today in class we learned how to find the opposite. What i mean by this is, the opposite in polynomials :D.
We first started off class by finding the opposite of easy stuff like:
ex. opposite of :
Mr.Backe the explained on finding the opposite of an expression. I will give an example first before i explain on how to get it :D
Lets assume x is 3.
This is how you simplify a simple one. What i did here was since the negative sign was outside of the brackets it applys to all of the numbers inside the brackets. Also a negative can't be all alone so really there is a 1 in front of the negative sign, which then makes it negative 1 -1. Since it applys to all numbers in the brackets you have to multiply -1 to 6 and 3.
Also the rules of multiplication with integers still applies. So if -1 is multiplying 6 its going to be -6 because when you multiply a negative and it is not the same sign it is always negative. You also do the same operation to the 3.
Mr Backe then gave us expressions that had trinomials or polynomials. For Example:
( 2x²-x-6) - (-3x² + 2x + 4 )
So again, since there is a negative sign in front of it that really means its -1. Now as i said before it applies to all numbers in the bracket.
Since the negative sign is in behind the second brackets that means it applies to only those numbers in the brackets.
You would then do these steps in order.
1. Apply to all numbers in brackets
2. Remove brackets
3. Gather like terms
If you follow these steps any questions like these will not give you a hard time. First you apply the negative sign to all numbers in brackets to get ...
Step 1 and 2 done: 2x² - x - 6 + 3x² - 2x - 4
Step 3: 2x² + 3x² - x - 2x - 6 - 4
Step 4: 5x² - 3x - 10
Also when you gather like terms you have to be careful when putting these numbers together.
As Mr.Backe said, the common mistake that, "kids" make is that when they collect like terms most "kids" would think for example 2x - 4 is 2x minus 4 when really its 2x NEGATIVE 4. vice versa :D just sayin.
If you follow these steps you should have no problem with any expressions. If this confuses you sorry ... this is the way i find out how to simplify these equations.
Also if i am missing anything please inform me :D. THNX
RATE AND COMMENT
especially comment if there is another way to find it :D.
PCE btw for homework. ahem *
5.3 Homework Book
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CYU #3, 4
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Pg. 204 Challenge for Hand-in