What is the result of multiplying 3a^5 by 2a^2 + 4a^2?

To find the product of the expressions 3a⁵ and 2a² + 4a², we can follow these steps:

1. First, distribute 3a⁵ to each term in the second expression.
2. The first term will be 3a⁵ * 2a².
3. The second term will be 3a⁵ * 4a².

Now let’s calculate each term:

• 3a⁵ * 2a² = 6a⁷ (because we add the exponents: 5 + 2 = 7)
• 3a⁵ * 4a² = 12a⁷ (again, adding the exponents: 5 + 2 = 7)

Now combine the results:

6a⁷ + 12a⁷ = 18a⁷

Therefore, the final product of 3a⁵ and 2a² + 4a² is 18a⁷.