Find in the simplest form: \( (3 x+2)\left(x^{2}+2 x-1\right) \)

To simplify the expression \( (3x + 2)(x^2 + 2x - 1) \), we will use the distributive property (also known as the FOIL method for binomials). First, distribute \(3x\) across the polynomial \(x^2 + 2x - 1\): \[ 3x \cdot x^2 = 3x^3, \] \[ 3x \cdot 2x = 6x^2, \] \[ 3x \cdot (-1) = -3x. \] Next, distribute \(2\) across the polynomial \(x^2 + 2x - 1\): \[ 2 \cdot x^2 = 2x^2, \] \[ 2 \cdot 2x = 4x, \] \[ 2 \cdot (-1) = -2. \] Now, we combine all these results: \[ 3x^3 + 6x^2 - 3x + 2x^2 + 4x - 2. \] Next, we combine like terms: \[ 3x^3 + (6x^2 + 2x^2) + (-3x + 4x) - 2 = 3x^3 + 8x^2 + x - 2. \] So, the expression in its simplest form is: \[ \boxed{3x^3 + 8x^2 + x - 2}. \]