SOLUTION: Hello, I am trying to figure out if I am on the right track. For some reason I just can't understand how to factor. Thanks in advance. 2t^2 y^4 - 32t^2 (I think at this point I

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, I am trying to figure out if I am on the right track. For some reason I just can't understand how to factor. Thanks in advance. 2t^2 y^4 - 32t^2 (I think at this point I       Log On


   

Question 221983: Hello, I am trying to figure out if I am on the right track. For some reason I just can't understand how to factor. Thanks in advance.
2t^2 y^4 - 32t^2 (I think at this point I can factor out the t^2)
t^2 (2y^4 - 32) (do I factor the parentheses at this point? I'm not sure where to go from here.)
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2t%5E2y%5E4-32t%5E2 Start with the given expression


2t%5E2%28y%5E4-16%29 Factor out the GCF 2t%5E2


Now let's focus on the inner expression y%5E4-16

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y%5E4-16 Start with the given expression.


%28y%5E2%29%5E2-16 Rewrite y%5E4 as %28y%5E2%29%5E2.


%28y%5E2%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.


Notice how we have a difference of squares. So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


%28y%5E2%2B4%29%28y%5E2-4%29 Factor the expression using the difference of squares.


You can then factor y%5E2-4 further (using the difference of squares rule described above) to get y%5E2-4=%28y%2B2%29%28y-2%29


So y%5E4-16 factors to %28y%5E2%2B4%29%28y%2B2%29%28y-2%29.


In other words y%5E4-16=%28y%5E2%2B4%29%28y%2B2%29%28y-2%29.
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So 2t%5E2%28y%5E4-16%29 then factors further to 2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29

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Answer:
So 2t%5E2y%5E4-32t%5E2 completely factors to 2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29


In other words, 2t%5E2y%5E4-32t%5E2=2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Missed it by THAT much.

Factoring out the was certainly the right thing to do, but if you notice, the numerical coefficients on the two original terms have the factor 2 in common. Hence, the correct first step would have been to factor out leaving you with:



But you aren't done, not by a long shot.

Notice that is the difference of two squares, so:



And then notice that is also the difference of two squares, so:



And that's as far as you can go presuming you are confining yourself to the real numbers.

John