You can check this answer by counting  the number of exponents in the first polynomial that add up to each exponent in the second polynomial, as follows:

The resulting polynomial after multiplying (1+t^3+t^6+...+t^30)(1+t^5+t^10+...+t^30) is: 1 + t^3 + t^5 + t^6 + t^8 + t^9 + 2t^10 + t^11 + t^12 + 2t^13 + 2t^15 + t^16 + 2t^17 + t^18 + 2t^19 + t^20 + 2t^21 + t^22 + 2t^23 + 2t^25 + t^26 + 2t^27 + t^28 + 2t^29 + t^30

Adding coefficients of like terms, we get:

1 + t^3 + 3t^5 + t^6 + 2t^8 + 2t^9 + 4t^10 + t^11 + t^12 + 4t^13 + 4t^15 + t^16 + 4t^17 + t^18 + 4t^19 + t^20 + 4t^21 + t^22 + 4t^23 + 4t^25 + t^26 + 4t^27 + t^28 + 4t^29 + t^30

Therefore, there are 28 monomials in the resulting polynomial.
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