How do I use the distributive law to factor 2a + 2b?

- anonymous

How do I use the distributive law to factor 2a + 2b?

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- anonymous

2(a+b)

- 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

What about 32x +4?

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- anonymous

well, what's the largest factor that is in both terms?

- anonymous

8?

- anonymous

8 doesn't go into 4 though. try a little smaller

- anonymous

2?

- anonymous

:) warmer? it's bigger than that.

- anonymous

4?

- 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

32/4 is 8 and 4/4 is 1....how would i write that out?

- anonymous

don't forget the x in the first term! but it will become 4(8x+1)

- anonymous

do you see what happened there? we can do more until you get a good handle on it.

- anonymous

Why is it written out like that...?

- 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

Ahhh, i see what you did now

- 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

so, for practice, factor this (it's a little different than the others):
3x^2+9x

- anonymous

first step; identify the largest factor which is in both

- anonymous

i'm gonna guess 1? 1 goes into all three?

- anonymous

oh wait i think you misread it. that 2 is an exponent. it's
\[3x^2+9x\]

- anonymous

sorry for the confusion

- anonymous

oh okay. so would it be 3?

- anonymous

and what would it look like after taking out the three?

- anonymous

what do you mean taking out?

- 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

so we divide x^2 by 3 and divide 9x by 3?

- anonymous

it was 3x^2, but yes that's correct

- anonymous

okay can we try 5x+10+15y? Because i dont really have any exponents in my homework yet.

- anonymous

oooh okay! i'm sorry. sure, give that one a try

- anonymous

Its fine. So, we divide by 5?

- anonymous

precisely

- anonymous

Would the answer be 5(1x+2+3y)?

- anonymous

yep, that's it! also, 1x is typically just written as x, but your answer is still right

- anonymous

Nice! Okay, so basically i just have to find the least factor for the numbers then divide by it?

- anonymous

greatest factor, actually. the least would be one :P

- anonymous

Okay. Is this correct, 7a+35b would be 7(a+5b)?

- anonymous

yes! :)

- anonymous

how about 7+7y? Would it be 7(7+y)?

- anonymous

you made a little error there; you see, if you multiply that out, you get 49+7y.

- anonymous

Okay, so how would i solve this one?

- 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

Lol, so would it be 7(y)? im not sure how to do this one

- 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

and you see that if you multiply out the right side using the distributive property, you do in fact get the left side.

- anonymous

Ohhhhhhhhhhhhhhh, alright, i got you

- anonymous

yay!

- 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

3(x+y) is what i ment

- 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

My homework says, List the factors in each expression and it gave me 3(x+y)

- anonymous

well, I suppose that means 3 is a factor and x+y is a factor?

- anonymous

Um, okay. i'm just gonna write that down & ask my professor tomorrow. Thanks for your help tho

- anonymous

yeah sure. I thought if they were asking that question though, they'd give it as 3x+3y, but whatever.

- anonymous

Yea, i don't know? i suck at math lol

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