SOLUTION: Is the following binomial a difference of squares 9a^2 - 8b^2? I have no idea how to even begin to approach this question. Obviously the answer yes or no would be appreicated, but

Algebra ->  Square-cubic-other-roots -> SOLUTION: Is the following binomial a difference of squares 9a^2 - 8b^2? I have no idea how to even begin to approach this question. Obviously the answer yes or no would be appreicated, but       Log On


   

Question 91621This question is from textbook Beginning Algebra
: Is the following binomial a difference of squares 9a^2 - 8b^2? I have no idea how to even begin to approach this question. Obviously the answer yes or no would be appreicated, but more importantly why it is such. Thank you in advance. This question is from textbook Beginning Algebra

Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Is:
9a%5E2-8b%5E2 a difference of squares?
Take a look at each of the two terms:
9a%5E2+=+%283a%29%5E2 This term is a perfect square.
8b%5E2+=+%282b%29%284b%29 This is not a perfect square:
So the answer is no!

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Is the following binomial a difference of squares 9a^2 - 8b^2
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yes and no
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No because the 8 in the 8b^2 terms is not a perfect square.
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Yes because, if radicals are allowed in the factoring,
9a^2-8b^2 could be factored as (3a-2bsqrt(2))(3a+2bsqrt(2))
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The fact of the matter is every binomial can be considered to
be a "difference of squares".
Even x-y can be factored as (sqrt(x)-sqrt(y))(sqrt(x)+sqrt(y))
but it is not considered to be a "difference of squares".
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My answer to your original question would be "no".
Cheers,
Stan H.