Which identity is the result of using the pythagorean theorem to show that a triangle with side lengths x^2 - 1, 2x, and x^2 + 1 is a right triangle? A. (x^2 - 1)^2 + (2x)^2 = -(x^2 + 1)^2
B. -(x^2 -1)^2 + (2x)^2 = (x^2 +1)^2
C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2
D. (x^2 - 1)^2 - (2x)^2 = (x^2 + 1)^2

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  C.  (x^2-1)^2 + (2x)^2 = (x^2 +1)^2

Step-by-step explanation:

Inexplicably, three of the four answer choices have minus signs in them. Those are all incorrect. The appropriate choice is ...

  C. (x^2-1)^2 + (2x)^2 = (x^2 +1)^2

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Expanded, this is ...

  x^4 -2x^2 +1 +4x^2 = x^4 +2x^2 +1 . . . . the desired identity

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: