Simplify $5(3-i)+3i(5-i)$.
$5(3-i) + 3i(5-i) = 15-5i + 15i - 3i^2 = 15 +10i -3(-1) = \boxed{18+10i}$.
18+10i
Level 3
Algebra
Problem: Simplify $5(3-i)+3i(5-i)$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To simplify the expression, first distribute the terms in the expression $5(3-i)$. This results in $15 - 5i$. Next, distribute the terms in the expression $3i(5-i)$. This gives $15i - 3i^2$. Since $i^2 = -1$, we can replace $-3i^2$ with $3$. Therefore, $3i(5-i)$ simplifies to $15i + 3$. 

Now, combine the results from both distributions: $15 - 5i + 15i + 3$. Group the real parts and the imaginary parts separately. The real parts are $15 + 3 = 18$. The imaginary parts are $-5i + 15i = 10i$. 

Thus, the final simplified expression is $18 + 10i$.<|END_OF_LATENT|> The final answer is $18+10i$.