Allison:
6(4)^2x+8 is rewritten as 6(r)^x+4. What is the value of r?
Allison:
@Hero
Hero:
\(6(4)^{2x+8} = 6(r)^{x+4}\) ?
Allison:
Yep
Hero:
Well, what happens if you factor out 2 from 2x + 8?
Hero:
Even clearer if you divide out the 6 first on both sides.
Allison:
x+8?
Allison:
So 6 is gone from both sides
Hero:
If you divide out the 6 on both sides you end up with \( 4^{2x+8}=r^{x+4}\)
Allison:
Yes
Hero:
So from there you would factor out the 2 from 2x + 8
Allison:
How
Hero:
Question: What happens if you apply the distributive rule to 3(x + 2) ?
Allison:
Rainbow multiply?
Hero:
Never heard of that, but what result do you get if you apply the distributive rule?
Allison:
3x+6?
Hero:
Correct, now what happens if you reverse that process you just performed?
Allison:
Reverse how
Hero:
By factoring.
Allison:
Omg how do I factor
Hero:
I gave you 3(x + 2). You performed the distributive rule to get 3x + 6.
Allison:
Right, rainbow method
Hero:
You got to that result by multiplying the x and the 2 by three.
Hero:
What is the inverse of multiplication?
Allison:
Division
Hero:
exactly
Allison:
What do I divide
Hero:
So when you factor, you're performing division.
Allison:
Right
Hero:
You divide 3x + 6 by 3 and then you write the result of that, then put the divisor on the outside of the parentheses.
Allison:
It's just 6
Hero:
So when you divide 3x+6 by 3, the result is x + 2. And then you put the three on the outside of the parentheses.
Allison:
!
Hero:
So you write 3(x + 2) which is what we started with.
Allison:
Ok
Allison:
What was the point of just going back to where we started?
Hero:
To show you how to factor
Allison:
Ok
Hero:
You asked "how do you factor"
Allison:
Ok now the actual doing of the problem
Hero:
That requires factoring 2x + 8
Hero:
Which requires knowing how to factor
Allison:
2(x+4)
Hero:
Congratulations. You did it.
Allison:
Thanks to you. Now what?
Hero:
I just hope you did it on your own strength.
Hero:
Now you have: \(4^{2(x+4)}=r^{x+4} \)
Allison:
You don't need strength to divide
Allison:
Yes
Hero:
Now it looks like we might be able to say what r is
Allison:
16?
Hero:
Correct
Allison:
Wow how easy
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