What is the product of (4s + 2) and (5s^2 + 10s + 3)?

1. Distribute the first term of the first binomial: Multiply $4s$ by each term in the second polynomial $(5s^2 + 10s + 3)$.
$4s \times 5s^2 = 20s^3$
$4s \times 10s = 40s^2$
$4s \times 3 = 12s$
So, the first part of the distribution is $20s^3 + 40s^2 + 12s$.

2. Distribute the second term of the first binomial: Multiply $2$ by each term in the second polynomial $(5s^2 + 10s + 3)$.
$2 \times 5s^2 = 10s^2$
$2 \times 10s = 20s$
$2 \times 3 = 6$
So, the second part of the distribution is $10s^2 + 20s + 6$.

3. Combine the results from both distributions: Add the terms obtained in step 1 and step 2.
$(20s^3 + 40s^2 + 12s) + (10s^2 + 20s + 6)$

4. Group like terms: Combine terms with the same variable and exponent.
$20s^3 + (40s^2 + 10s^2) + (12s + 20s) + 6$

5. Simplify by adding like terms:
$20s^3 + 50s^2 + 32s + 6$