Which expression is equivalent to \( \left(2 x^{2}+3\right)(x+4) \) ? (A) \( 2 x^{3}+12 \) (B) \( 2 x^{2}+11 x+12 \) (C) \( 2 x^{3}+6 x^{2}+4 x+12 \) (D) \( 2 x^{3}+8 x^{2}+3 x+12 \)

To find the expression equivalent to \( \left(2 x^{2}+3\right)(x+4) \), we can use the distributive property (also known as the FOIL method for binomials). First, distribute \( 2x^2 \) to both terms in \( (x + 4) \): \[ 2x^2 \cdot x + 2x^2 \cdot 4 = 2x^3 + 8x^2. \] Next, distribute \( 3 \) to both terms in \( (x + 4) \): \[ 3 \cdot x + 3 \cdot 4 = 3x + 12. \] Now, combine all the terms: \[ 2x^3 + 8x^2 + 3x + 12. \] Thus, the final expression is \( 2x^3 + 8x^2 + 3x + 12 \). The correct answer is (D) \( 2 x^{3}+8 x^{2}+3 x+12 \). Have fun with polynomials—they can be as lively as a dance floor if you know the steps! Remember, mastering the basics of distribution can help you breeze through complex expressions with ease!