Simplify the expression $3a(4a-1) + 2a(a+3) - 5a(2a-1)$.

1. Problem Description

Simplify the expression $3a(4a-1) + 2a(a+3) - 5a(2a-1)$.

2. Solution Steps

First, distribute $3a$ to $(4a-1)$:

$3a(4a - 1) = 3a(4a) - 3a(1) = 12a^2 - 3a$

Next, distribute $2a$ to $(a+3)$:

$2a(a+3) = 2a(a) + 2a(3) = 2a^2 + 6a$

Then, distribute $-5a$ to $(2a-1)$:

$-5a(2a - 1) = -5a(2a) - 5a(-1) = -10a^2 + 5a$

Now, combine the results:

$12a^2 - 3a + 2a^2 + 6a - 10a^2 + 5a$

Combine like terms:

$(12a^2 + 2a^2 - 10a^2) + (-3a + 6a + 5a) = (12+2-10)a^2 + (-3+6+5)a = 4a^2 + 8a$

3. Final Answer

$4a^2 + 8a$