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each term has a 2 in it, so you can take that out of it. dividing each term by 2 leaves (a+b) inside. so we have 2a+2b=2(a+b)
What about 32x +4?
well, what's the largest factor that is in both terms?
8 doesn't go into 4 though. try a little smaller
:) warmer? it's bigger than that.
precisely. now, divide each term by 4, and this is what will be left inside the parentheses, and you take the four out.
32/4 is 8 and 4/4 is 1....how would i write that out?
don't forget the x in the first term! but it will become 4(8x+1)
do you see what happened there? we can do more until you get a good handle on it.
Why is it written out like that...?
because now, because of the distributive law, the 4 will be distributed to both of the terms. that means we will get 4(8x+1)=4*8x+4*1=32x+4 which is what we started with
Ahhh, i see what you did now
and notice that 8x and 1 don't have any common factors that we can take out; the idea is to take out the "biggest" thing we possibly can
so, for practice, factor this (it's a little different than the others): 3x^2+9x
first step; identify the largest factor which is in both
i'm gonna guess 1? 1 goes into all three?
oh wait i think you misread it. that 2 is an exponent. it's \[3x^2+9x\]
sorry for the confusion
oh okay. so would it be 3?
and what would it look like after taking out the three?
what do you mean taking out?
the idea is, once we find the largest thing, you "take it out" by putting the thing in parentheses, moving the thing outside of the parentheses, and dividing each term inside by whatever you took out
so we divide x^2 by 3 and divide 9x by 3?
it was 3x^2, but yes that's correct
okay can we try 5x+10+15y? Because i dont really have any exponents in my homework yet.
oooh okay! i'm sorry. sure, give that one a try
Its fine. So, we divide by 5?
Would the answer be 5(1x+2+3y)?
yep, that's it! also, 1x is typically just written as x, but your answer is still right
Nice! Okay, so basically i just have to find the least factor for the numbers then divide by it?
greatest factor, actually. the least would be one :P
Okay. Is this correct, 7a+35b would be 7(a+5b)?
how about 7+7y? Would it be 7(7+y)?
you made a little error there; you see, if you multiply that out, you get 49+7y.
Okay, so how would i solve this one?
7 is the greatest common factor of the two terms, but when you divide 7 by 7, you get 1. The y part is correct.
Lol, so would it be 7(y)? im not sure how to do this one
ok, our two terms are 7 and 7y, and the factor we're taking out is 7. so, when we divide 7 by 7, we get 1. This doesn't mean it disappears, it's just 1. 7y divided by 7 gives y, and so we have that 7+7y=7(1+y)
and you see that if you multiply out the right side using the distributive property, you do in fact get the left side.
Ohhhhhhhhhhhhhhh, alright, i got you
OKay, i got another question lol. How do i list factors in an expression. 3(x_y) would the factors be 3 & x? since those are the only ones being multiplied?
3(x+y) is what i ment
what do you mean, list factors in it? the way you have it written, that expression is already factored, and its factors are 3 and x+y
My homework says, List the factors in each expression and it gave me 3(x+y)
well, I suppose that means 3 is a factor and x+y is a factor?
Um, okay. i'm just gonna write that down & ask my professor tomorrow. Thanks for your help tho
yeah sure. I thought if they were asking that question though, they'd give it as 3x+3y, but whatever.
Yea, i don't know? i suck at math lol