OK, it's not like me to do this, but I'm giving this one away.
If you had
you could just factor out the
(GCF) and be left with
. You've just factored out the highest thing you have. And is not 4 just (3 + 1)? Therefore in this example b = 3 and b+1 is 4.
allows me to factor out the
to have
Every time my left term is one bigger than my right, I can factor out the degree over on the right one, which leaves me with an exponent of 1 on the left one. Every time.
If the left one is (b + 1), it's one bigger than the one on the right term, so you can always factor out as many as are on the right term, leaving 1 on the left one.
And this:
take the x to b+1 and distribute it to get xb +x1
is not "distributing" and you aren't multiplying.
It would be useful if you'd at least use ^ for exponents so that we know what you mean.
Do you mean
? If so, then write it (x^b) - (x^1) to make it clear what you are doing.
But since you're calling it "distributing" and mentioning multiplying, and also saying "so there's no exponents," I have to wonder if you mean
exactly like it looks. And no, you can't do that. It isn't
so that you can distribute. The (b+1) is an exponent.
Think backwards:
. That's a rule you have.
Cause for example:
means
, and since I can remove all those parenthesis, essentially I have x multiplied times itself 7 total times.
Hence:
=
=
- you can just add the exponents cause that's how many times total you're going to multiply x times itself.
Therefore, I can also do it backwards:
=
.
But I'm not "distributing" it, like multiplying the x times the 3 and then times to 4, cause I'm not multiplying. They're exponents.
You can do the same thing with the
as what I did with the 3 and 4 above.
Once that is done, you still have to carry down the "- x" that's on the end of it -- you can't just drop that off.
Once you have
, it can be rewritten without the * in there, and without the 1 exponent, which is understood:
. Tack on that "- x" and start factoring.
I personally think this is just the hard way about it, but you may have to show this work.