x * 2x = 2x^2 (check)

5x^3 + 2x^5 = ?

Can you add these two?

yes, x(2x) = 2x^2

for the 2nd, we cannot add "unlike" terms, one is x^3, the other is x^5, not the same

So, what if there was a multiplication sign instead of the addition sign? Then would the answer be 10x^8?

yes

To add the expressions 5x^3 and 2x^5, you need to first identify the terms with similar exponents. In this case, the terms are not like terms because the exponents (3 and 5) are different. Therefore, you cannot directly combine them like you could with similar terms.

To simplify the expression, you just write it as it is:

5x^3 + 2x^5

Since there are no like terms, this is the simplest form of the expression.

Thus, the simplified expression is 5x^3 + 2x^5.