Multiplying polynomials in Mathematica

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To multiply the polynomials (1+x+x^2+x^3) and (1+x+x^2+x^3+x^4) in Mathematica, the correct command is Expand[(1+x+x^2+x^3)*(1+x+x^2+x^3+x^4)]. Users may encounter issues if they do not use the Expand function properly. Ensuring that the syntax is correct is crucial for obtaining the desired product. The discussion highlights the importance of understanding Mathematica's functions for polynomial operations. Properly applying the Expand function will yield the correct result for the polynomial multiplication.
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I have two polynomials

(1+x+x^2+x^3) and (1+x+x^2+x^3+x^4), I'm trying to figure out how to compute the product in Mathematica, but it's not working.

Any help is appreciated, thanks.
 
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Expand[(1+x+x^2+x^3)*(1+x+x^2+x^3+x^4)]
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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