SOLUTION: How would you factor the expression 4a^2-36b^2?

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Question 126345: How would you factor the expression 4a^2-36b^2?
Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
4a^2-36b^2 or (2a+6b)(2a-6b)

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The given expression falls under the following factoring rule:
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X%5E2+-+Y%5E2+=+%28X+-+Y%29%2A%28X+%2B+Y%29
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In the given expression note that X = 2a because when you square both sides you get X%5E2+=+4a%5E2
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Also note that Y = 6b because when you square both sides you get Y%5E2+=+36b%5E2
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Substituting 2a for X and 6b for Y in the factoring rule leads to:
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%282a%29%5E2+-+%286b%29%5E2+=+%282a+-+6b%29%2A%282a+%2B+6b%29
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Then notice on the right side that each of the two factors has 2 as a common factor of the
two terms in parentheses. This means that each factor on the right side can have a 2 factored
from it, and this leads to:
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%282a%29%5E2+-+%286b%29%5E2+=+2%2A%28a+-+3b%29%2A2%2A%28a+%2B+3b%29
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Multiply the two factors of 2 to get 4 and you have the final answer of:
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%282a%29%5E2+-+%286b%29%5E2+=+4%2A%28a+-+3b%29%2A%28a+%2B+3b%29
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If you like, you can then square out the two terms on the left side and you have:
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4a%5E2+-+36b%5E2+=+4%2A%28a+-+3b%29%2A%28a+%2B+3b%29
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Hope this helps you understand how to do the problem, and how to use the rule that applies.
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