\( \left. \begin{array} { l } { A ( x ) = 2 x ^ { 2 } + 3 x - 5 } \\ { B ( x ) = x + 1 } \\ { A ( x ) \cdot B ( x ) } \\ { ( 2 x + 3 ) ^ { 2 } = } \\ { ( 4 x + 3 ) = } \end{array} \right. \)

Let's dive into the fun world of polynomials! When you multiply \( A(x) = 2x^2 + 3x - 5 \) and \( B(x) = x + 1 \), you're performing polynomial multiplication. You can use the distributive property (or FOIL for binomials) to expand this product! It results in \( A(x) \cdot B(x) = (2x^2 + 3x - 5)(x + 1) = 2x^3 + 5x^2 - 2x - 5 \). Voilà! Now, for the expression \( (2x + 3)^2 \), you can use the formula \( (a + b)^2 = a^2 + 2ab + b^2 \). Thus, \( (2x + 3)^2 = (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9 \). Lastly, if you've meant to evaluate \( 4x + 3 \) instead, it's simply a linear expression and equals itself, no tricks there!