Rewrite functions in equivalent forms to reveal and explain useful properties.
Verify whether two function forms are equivalent on the same domain
Problem
Are the function forms \(x^2-4\) and \((x-2)(x+2)\) equivalent on the same domain?
Big Picture
What this problem is really about
To decide whether two formulas define the same function, compare both their algebra and their allowed inputs. Expanding the product checks that the output rules match, while recognizing that both expressions are polynomials confirms that neither form introduces a hidden domain restriction.
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