SOLUTION: factor 75r^2-48

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Question 190751: factor
75r^2-48
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

75r%5E2-48 Start with the given expression


3%2825r%5E2-16%29 Factor out the GCF 3


Now let's focus on the inner expression 25r%5E2-16




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25r%5E2-16 Start with the given expression.


%285r%29%5E2-16 Rewrite 25r%5E2 as %285r%29%5E2.


%285r%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=5r and B=4.


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.


%285r%29%5E2-%284%29%5E2=%285r%2B4%29%285r-4%29 Plug in A=5r and B=4.


So this shows us that 25r%5E2-16 factors to %285r%2B4%29%285r-4%29.


In other words 25r%5E2-16=%285r%2B4%29%285r-4%29.


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Answer:
So 75r%5E2-48 factors to 3%285r%2B4%29%285r-4%29