Multiply (a+b+2c)(3a-2b): Expanding Two-Factor Polynomial Expression

To solve the expression $(a+b+2c)\cdot(3a-2b)$, we will apply the distributive property.

• Step 1: Distribute each term of the first expression to every term of the second expression.

• Step 2: Compute the resulting products.

• Step 3: Combine like terms.

Let's execute these steps:
Step 1: Distribute:
Distribute $a$: $a \cdot 3a + a \cdot (-2b) = 3a^2 - 2ab$
Distribute $b$: $b \cdot 3a + b \cdot (-2b) = 3ab - 2b^2$
Distribute $2c$: $2c \cdot 3a + 2c \cdot (-2b) = 6ac - 4bc$

Step 2: Add all these products together:
$3a^2 - 2ab + 3ab - 2b^2 + 6ac - 4bc$

Step 3: Combine like terms:
Combine $-2ab + 3ab$ to get $ab$.

Therefore, the simplified expression is:
$3a^2 + ab - 2b^2 + 6ac - 4bc$.

The correct choice is 4.

Thus, the final expanded expression is $3a^2 + ab - 2b^2 + 6ac - 4bc$.