Simplify (x+3)4x+2: Applying the Distributive Property

Let's analyze the expression step-by-step:

The original expression is $(x+3)4x + 2$.

• Step 1: Apply the distributive property to the first part of the expression, $(x+3)4x$.
• First, distribute $4x$ to $x$:
  $4x \cdot x = 4x^2$.
• Then, distribute $4x$ to $3$:
  $4x \cdot 3 = 12x$.
• Therefore, by applying the distributive property, $(x+3)4x = 4x^2 + 12x$.
• Step 2: Add the remaining term in the expression, which is $+ 2$.

Combining all the parts together gives:

$4x^2 + 12x + 2$

With these calculations, we can clearly see that the distributive property has been applied correctly and the fully simplified expression is:

$4x^2 + 12x + 2$

Reviewing the multiple-choice answers, the option that aligns with our calculated expression and indicates a "No" response for incorrectly applying distributive property is:

No, $( 4x^2 + 12x + 2 )$

Thus, the correct choice is option 2.