SOLUTION: Find the products. a(a+5)(a-5)

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Question 112672: Find the products.
a(a+5)(a-5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%28a%2B5%29%28a-5%29 Start with the given expression


%28a%5E2%2B5a%29%28a-5%29 Distribute



Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:%28a%5E2%29%2A%28a%29=a%5E3


Multiply the Outer terms:%28a%5E2%29%2A%28-5%29=-5a%5E2


Multiply the Inner terms:%285a%29%2A%28a%29=5a%5E2


Multiply the Last terms:%285a%29%2A%28-5%29=-25a


a%5E3-5a%5E2%2B5a%5E2-25a Now collect every term to make a single expression



a%5E3-25a Now combine like terms


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Answer:
So %28a%5E2%2B5a%29%28a-5%29 foils and simplifies to a%5E3-25a

In other words, %28a%5E2%2B5a%29%28a-5%29=a%5E3-25a

Notice how a%5E3-25a factors back to the original expression %28a%5E2%2B5a%29%28a-5%29 (if you need help with factoring, check out this solver). So this verifies our answer.