anonymous
  • anonymous
How do I use the distributive law to factor 2a + 2b?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
2(a+b)
anonymous
  • anonymous
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)
anonymous
  • anonymous
What about 32x +4?

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

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