Multiply (4y+3)(3x+2): Binomial Expression Expansion

To solve this problem, we'll expand and simplify the expression $(4y + 3)(3x + 2)$ by applying the distributive property. Let's go through the steps:

• Step 1: Use the distributive property on $(4y + 3)(3x + 2)$.
• Step 2: Multiply each term in $(4y + 3)$ with each term in $(3x + 2)$.
• Step 3: Combine like terms if possible.

Now, let's perform these steps in detail:

Step 1: The expression is given as $(4y + 3)(3x + 2)$. We'll expand this by multiplying each component:

$4y \cdot 3x = 12xy$
$4y \cdot 2 = 8y$
$3 \cdot 3x = 9x$
$3 \cdot 2 = 6$

Step 2: Combine all these products to form the expanded expression:

$12xy + 8y + 9x + 6$

Step 3: Verify if we can combine any like terms. In this case, all terms are different, so no combination is possible.

Thus, the simplified result of the expression $(4y+3)(3x+2)$ is: $12xy + 8y + 9x + 6$.

This matches choice 1 from the provided options.