Factor this expression. Check by multiplying factors.
3ab+3ac+2b^2+2bc

- anonymous

Factor this expression. Check by multiplying factors.
3ab+3ac+2b^2+2bc

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- katieb

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- Mertsj

Are you learning how to do these? You keep posting the same type of problem.

- anonymous

Not at all.

- Mertsj

Do you want to learn?

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## More answers

- anonymous

I would love to.

- Mertsj

Take the first two terms: 3ab +3ac
What do they have in common?

- anonymous

Do you have Skype so we don't spam this feed?

- Mertsj

No I don't

- anonymous

Ok well they share "a"

- Mertsj

What else do they share?

- anonymous

3

- Mertsj

Good. so factor out 3a and tell me what you get

- anonymous

1,3

- Mertsj

|dw:1327549920542:dw|

- Mertsj

Do you understand that?

- anonymous

Yes

- Mertsj

Now take the last two terms which are 2b^+2bc
What do they have in common?

- anonymous

2b

- Mertsj

Factor it out

- anonymous

|dw:1327550017696:dw|

- Mertsj

Factor out 2b. Not just 2

- Mertsj

You said they have 2b in common and they do. So factor out 2b

- anonymous

|dw:1327550097535:dw|

- Mertsj

|dw:1327550099915:dw|

- Mertsj

I think that was my fault because I didn't get the exponent on the 2b^2

- anonymous

Hmm.

- Mertsj

|dw:1327550268634:dw|

- Mertsj

So you see that now we have 2 terms instead of 4?

- anonymous

Yes.

- Mertsj

And what do those two terms have in common?

- anonymous

b

- Mertsj

|dw:1327550319609:dw|

- Mertsj

Do you see that they have (b+c) in common?

- anonymous

Yeah

- Mertsj

Factor it out.

- anonymous

Factor out 9\b+c?)\

- anonymous

Wow, backspace is retartded

- Mertsj

What did you say they have in common/

- anonymous

b+c

- Mertsj

Then factor out b+c

- anonymous

They're alreadty factored out. Is your backspace working? Mine won't work on this website but others it will.

- Mertsj

b+c times something equals the first term which is 3a(b+c)

- Mertsj

Yes my backspace works.

- Mertsj

Would you agree that (b+c)(3a )=3a(b+c)?

- anonymous

Yes.

- Mertsj

Now consider the second term 2b(b+c)
(b+c) times something = 2b(b+c) What is it?

- anonymous

2

- Mertsj

2(b+c) does not equal 2b(b+c)

- anonymous

2b

- Mertsj

Yes. So now put it all together. Look at the drawing.

- Mertsj

And think of (b+c) as a unit.

- Mertsj

|dw:1327550434478:dw|

- anonymous

|dw:1327550790530:dw|

- anonymous

Messed up on the drawing.

- Mertsj

Do you see that (b+c)(3a) gives the first term and (b+c)(2b) gives the second term/

- anonymous

Yes.

- Mertsj

And now it is factored because it is only one term

- Mertsj

now if you have another problem like that, you should try it yourself. And if you don't have another one, you should go back and try to understand the others that you posted.
It's called "factoring by grouping"

- anonymous

ok

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