SOLUTION: i seem to be having trouble can i please have help? 4s^2-100t^2 thank you for your time

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Question 179427: i seem to be having trouble can i please have help?
4s^2-100t^2
thank you for your time
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4s%5E2-100t%5E2 Start with the given expression


4%28s%5E2-25t%5E2%29 Factor out the GCF 4


Now let's focus on the inner expression s%5E2-25t%5E2


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s%5E2-25t%5E2 Start with the inner expression.


%28s%29%5E2-25t%5E2 Rewrite s%5E2 as %28s%29%5E2.


%28s%29%5E2-%285t%29%5E2 Rewrite 25t%5E2 as %285t%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=s and B=5t.


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


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%28s%29%5E2-%285t%29%5E2=%28s%2B5t%29%28s-5t%29 Plug in A=s and B=5t.


So this shows us that s%5E2-25t%5E2 factors to %28s%2B5t%29%28s-5t%29.


In other words s%5E2-25t%5E2=%28s%2B5t%29%28s-5t%29.
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So this means that 4%28s%5E2-25t%5E2%29 factors down further to 4%28s%2B5t%29%28s-5t%29



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Answer:

So 4s%5E2-100t%5E2 completely factors to 4%28s%2B5t%29%28s-5t%29