SOLUTION: Factor completely: 25x^2-4/49 Thanks for the help

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Question 182029This question is from textbook
: Factor completely:
25x^2-4/49
Thanks for the help This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2-4%2F49 Start with the given expression.


%285x%29%5E2-4%2F49 Rewrite 25x%5E2 as %285x%29%5E2.


%285x%29%5E2-%282%2F7%29%5E2 Rewrite 4%2F49 as %282%2F7%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=5x and B=2%2F7.


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.


%285x%29%5E2-%282%2F7%29%5E2=%285x%2B2%2F7%29%285x-2%2F7%29 Plug in A=5x and B=2.


So this shows us that 25x%5E2-4%2F49 factors to %285x%2B2%2F7%29%285x-2%2F7%29.


In other words 25x%5E2-4%2F49=%285x%2B2%2F7%29%285x-2%2F7%29.