Question

factor completely and show steps:
2((x+4)^1/2)(2)((3x-2)^3)+((x+4)^-1/2)((3x-2)^4)(1/3)

Answer 1

Marissa, even tho' it'd take you some time to learn how to use Equation Editor (below), it'd be a wise investment of time and effort. Although you've done a nice job of separating terms using parentheses and to indicate order of operations, the reader still has to do considerable deciphering, and to make assumptions, to translate 2((x+4)^1/2)(2)((3x-2)^3)+((x+4)^-1/2)((3x-2)^4)(1/3) into more conventional symbols.

Answer 2

2((x+4)^1/2)(2)((3x-2)^3)+((x+4)^-1/2)((3x-2)^4)(1/3)

\[2(x+4)^{^{?}}*2*(3x-2)^{3} \] and so on.

Answer 3

To factor 2((x+4)^1/2)(2)((3x-2)^3)+((x+4)^-1/2)((3x-2)^4)(1/3), we'll need to work our way through this expression (or one typed in Equation Editor), identify any common factors, and factor them out.

See any common factors in 2((x+4)^1/2)(2)((3x-2)^3)+((x+4)^-1/2)((3x-2)^4)(1/3) ?

Answer 4

\[2(x+4)^{1/2}(2)(3x-2)^{3}+(x+4)^{-1/2}(3x-2)^{4}(1/3)\]

Answer 5

@mathmale yeah i know how to use it once it gets into a discussion thing like this but i don't know how to pull it up when I'm first posting a question lol

Answer 6

At the bottom of the right-hand column of OpenStudy's web page, you'll see 3 blue buttons. Just click on Equation when you're ready to use Equation Editor.

Thanks for doing such a lovely job of typing out your whole expression in Equation Editor.

Now please look through what you've typed and identify one factor common to both terms. Factor that out. Then look again for another factor common to both terms. Factor that out. Does this make sense to you?

Answer 7

so i get that i can factor out \[(x+4)^{1/2} (3x-2)^{3}\] but idk how to show the rest left

Answer 8

@mathmale

Answer 9

I'd agree that you CAN factor out (3x-2)^3, but not (x+4)^(1/2), because one of the exponents of (x+4) happens to be negative. Any idea regarding what to do in a case like this?

Answer 10

Hope the following makes sense to you:

1. Factor out (3x-2)^3. The other factor has two terms involving (x+4).
2. Multiply this other factor by Sqrt(x+4), and then divide (3x-2)^3 by Sqrt(x+4). This is, of course, equivalent to multiplying by 1. Advantage? You will have removed Sqrt(x+4) from the 2-term second factor.
3. Simplify the 2-term second factor by combining like terms.

4. Write the final result as

[(3x-2)^3]
------------ * [2-term second factor, simplified by combining like terms].
Sqrt(x+4)

Answer 11

Very happy to work with you. Unfortunately, it's late where I am and I need to hit the sack. If you choose to respond, I'll see your response in the morning.

Answer 12

sorry i was trying to follow you on that stuff. thank you very much for the help!

Answer 13

@whpalmer4 factor completely:
2(x+4)1/2(2)(3x−2)3+(x+4)−1/2(3x−2)4(1/3)

Answer 14

\[2(x+4)^{1/2}(2)(3x-2)^{3}+(x+4)^{-1/2}(3x-2)^{4}(1/3)\]