SOLUTION: what is the factored form of 4w^2 - 225

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Question 263196: what is the factored form of
4w^2 - 225
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4w%5E2-225 Start with the given expression.


%282w%29%5E2-225 Rewrite 4w%5E2 as %282w%29%5E2.


%282w%29%5E2-%2815%29%5E2 Rewrite 225 as %2815%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=2w and B=15.


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.


%282w%29%5E2-%2815%29%5E2=%282w%2B15%29%282w-15%29 Plug in A=2w and B=15.


So this shows us that 4w%5E2-225 factors to %282w%2B15%29%282w-15%29.


In other words 4w%5E2-225=%282w%2B15%29%282w-15%29.