To multiply the polynomials (1-2t)(5t+t^2), we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:
(1-2t)(5t+t^2) = 1(5t+t^2) - 2t(5t+t^2)
Multiplying the first term by each term in the second polynomial, we get:
5t + t^2
Multiplying the second term by each term in the second polynomial, we get:
-10t^2 - 2t^3
Combining like terms, we get:
-2t^3 - 10t^2 + 5t
Therefore, the answer is D. -2t^3 - 9t^2 + 5t.