Solve the Binomial Expression: Expanding (4a-b)(b+3a)

To solve this problem, we will expand the expression $(4a-b)(b+3a)$ using the distributive property:

Firstly, use the distributive property to expand:

• Step 1: Distribute $4a$ across both terms in $(b + 3a)$:
  $4a \cdot b = 4ab$ and $4a \cdot 3a = 12a^2$
• Step 2: Distribute $-b$ across both terms in $(b + 3a)$:
  $-b \cdot b = -b^2$ and $-b \cdot 3a = -3ab$

Combine all these terms:

$4ab + 12a^2 - b^2 - 3ab$

Combine like terms:

• The terms $4ab$ and $-3ab$ combine to give $ab$.

Thus, the simplified form of the expression is:

$12a^2 - b^2 + ab - ab = 12a^2 - b^2 - ab$

Therefore, the solution to the problem is $12a^2 - b^2 - ab$, which corresponds to choice 2.