Multiplying and Dividing Monomials
Today Mr.Backe gave us a question when we were seated. His question to us was
- (6x +7)
- notice that the "-" is spaced out because right there is the "1" beside it, You just don't see it but its there because mathematicians are lazy and they leave a space beside the "-" and the bracket.
Also notice that this is a binomial question because you'll be doing this on a quiz I think.
- (6x +7) = -1 (6x+7)
= -1 (6x) + (-1)(+7) (second step)
= -6x -7
Notice the (+) is placed there as well as (-1) at the second step. It was put there because you know that by doing the first step the (-1) stays the same because your adding the +7 and that is why -1 is beside +7 (hope I explained it well enough for you guys to know).
The "+" is moved down to the second step because your adding the other side (I also hope I explained it well). (-1)(+7) multiply each other just letting you know and the "-" stay "-".
The third step is the answer because the -1 and 6x "fuse" together to make up a -6x and -1+7 equal up to a -7 so yea the answer is -6x -7. That is called Distributive Property which you learned but I'm typing it down anyway so yea.
Distributive Property means that we distributed the negative one over both terms of the binomial.
More questions Mr.Backe gave us and that we learn how to do it is 2 (2x)
The 2 (2x) means that you have "2" groups of "2x" meaning those tiles, but I cant draw or computer it because I don't know how you guys would see it, but I'll give out the answers
2 ( 2x) = 4x because your multiplying them
More questions Mr.Backe gave us which took us an easy time but sometimes hard for others like Asham just kidding. Just giving the answer.
-3x (2x) = (-3x)(2)(x)(x)
= -6x squared
2(2x) = (2)(2)(x)(x)
= 4x squared
3x(2x) = (3)(2)(x)(x)
= 6x squared
-3x(-2x) = (-3x)(-2x)(x)(x)
= 6x squared
Exact procedure but different statement.
Mr.backe added a "y"
(2x) (2y) = (2)(2)(x)(y)
your just adding in the "y" variable
(2xy) (2x) = (2)(x)(y)(2)(x)
notice that I'm doing it in the exact order and now your finding "like" terms
= 4x squared y
(3x) (3xy) = (3)(x)(3)(x)(y)
= 9x squared y
Now its negative 2
(4xy) (-2xy) = (4)(x)(y)(-2)(x)(y)
Notice that I'm highlighting the 4 and negative 2 because the negative sign stays the same even if the 4 is a positive (hard to explain) -_-
= -8x squared y squared
Mr.Backe taught us how to divide polynomials and this is the question he gave us
6x over 2 = 3x, In order to find that answer you gotta do this,
Start with the question, 6x over 2 then you use the procedure (which I mentioned)
6x over 2 = 6 (x) over 2 (x) Multiply them and you get 3x squared but you can just basically cross the answer and the denominator to get the original number (6x)
Here's an easy one Mr.Backe gave us
6x squared over 2x
= 6x(x)(x) over 2(x)
9x squared over 3x = 9 (x)(x) over 3 (x)
Your dividing the number and your crossing out one "x" leaving out one x in 9, the denominator is the same so its 3x because 9 over 3 is 3.
-extra practise 7.1
-self check ALL OF IT!!!!!!!!!!, oh and don't forget to do them in case you missed what's yesterdays homework.
If I have made any mistakes please correct me
Next scribe is John Pangan ! :)