Question

How to factor the expression completely:
((1+(4/x))^2)+((1-(4/x))^2)

Answer 1

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

Answer 2

Is that the problem?

Answer 3

Yes it is

Answer 4

Actually the (^2) is on the outside of the parentheses.

Answer 5

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

Answer 6

Is that it?

Answer 7

Yes! Sorry for the confusion..

Answer 8

Expand each binomial and collect the like terms.

Answer 9

Does that simplify to 16/x?

Answer 10

I am so sorry again, but there's supposed to be a minus between the two quantities.. I got mixed up after all the parentheses

Answer 11

\[1+\frac{8}{x}+\frac{16}{x^2}+1-\frac{8}{x}+\frac{16}{x^2}\]

Answer 12

Collect the like terms.

Answer 13

With the minus in between I get 16/x? Is that the answer then?

Answer 14

yes

Answer 15

Thank you so much!

Answer 16

yw

Answer 17

Could you help with another problem?

Answer 18

Only if you double check to make sure you have posted it correctly before I work on it.

Answer 19

I will. I'll attach the file, thank you.

Answer 20

The problem is in the attachment

Answer 21

Factor out:
\[(\frac{1}{2}x ^{-\frac{1}{2}})(7x+4)^{-\frac{1}{2}}\]

Answer 22

That's the first portion of the problem right?

Answer 23

It says to factor completely. That is what I would do as a first step is factor out those two common factors.

Answer 24

How do I factor out the (7x+4)^(-1/2) if the first one is positive?