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I was wondering if you could explain to me how to multiply and factor?
Things like this:
Multiply:
(2x)(3x)(4x)
and
2xy(x - y)
and
(x+2)(x+5)
Factor:
2x^3 - 6x
and
x^2y+xy^2
I have a whole page I'm supposed to do but I have no idea how =[
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Hello.
To do the first problem, you have to multiply like terms. So since they are already like terms [all are in terms of x].
So you would first multiply 2x by 3x and you first multiply the 2 and the 3 to get 6 and then the two xs to get x^2. So put them together to get 6x^2. Then you still have to multiply that by the 4x. So 6 times 4 to get 24, then x^2 by x and you get x^3. So together you get 24x^3 and that's your answer.
For the second problem, you have to distribute.
So first you have to multiply the x in the parentheses by everything outside of it.
So x times 2xy is 2x^2y, because you only multiply the xs when the "2xy" is a number together.
Remember when you multiply the "y" by the "2xy", the y is actually negative. So then you put the negative sign in front of that entire number, making it -2xy^2.
Then you combine your two numbers to get the answer:
2x^2y-2xy^2
For the third one, use something teachers often refer to as the FOIL method. That's First, Outer, Inner, Last.
So multiply the First two terms by each other:
x times x is...
Then do the Outer terms:
x times 5 is...
Then do the Inner terms:
2 times x is...
Then do the Last terms:
2 times 5 is...
Then, combine like terms, and your answer should look like this:
x^2+7x+10
For the first factoring problem, what you have to do is "take out" a number or variable that is common in each term of the problem.
So between 2x^3 and 6x, what is common? They both have xs and they both have a 2 in them [6x can be thought of as 2x times 3]. So take out "2x" from each.
That leaves 2x^3 to be x^2.
That leaves 6x to be 3.
So...
2x^3-6x can be factored to be:
2x (x^2 - 3)
Do the same thing for the last problem. Find something common between the terms.
Each one has an x and a y. So the common term is xy.
Take "xy" out of each of the terms and it should come out to be...
x^2y --> x
xy^2 --> y
So your factors are:
(xy)(x + y)
I hope you followed that. Notice how I didn't just tell you the answer, I let you know how to do it. =]
Thanks for inboxing.
--Jack
(16/m)
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