Question

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

Answer 1

2(a+b)

Answer 2

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)

Answer 3

What about 32x +4?

Answer 4

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

Answer 5

8?

Answer 6

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

Answer 7

2?

Answer 8

:) warmer? it's bigger than that.

Answer 9

4?

Answer 10

precisely. now, divide each term by 4, and this is what will be left inside the parentheses, and you take the four out.

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

Why is it written out like that...?

Answer 15

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

Answer 16

Ahhh, i see what you did now

Answer 17

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

Answer 18

so, for practice, factor this (it's a little different than the others):

3x^2+9x

Answer 19

first step; identify the largest factor which is in both

Answer 20

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

Answer 21

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

Answer 22

sorry for the confusion

Answer 23

oh okay. so would it be 3?

Answer 24

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

Answer 25

what do you mean taking out?

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

Its fine. So, we divide by 5?

Answer 32

precisely

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

yes! :)

Answer 39

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

Answer 40

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

Answer 41

Okay, so how would i solve this one?

Answer 42

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.

Answer 43

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

Answer 44

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)

Answer 45

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

Answer 46

Ohhhhhhhhhhhhhhh, alright, i got you

Answer 47

yay!

Answer 48

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?

Answer 49

3(x+y) is what i ment

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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