Find the product. Simplify your answer. \( (2 m-1)\left(-3 m^{2}+2 m+1\right) \)

To find the product \( (2m - 1)(-3m^2 + 2m + 1) \), we can use the distributive property, also known as the FOIL method for binomials. 1. Multiply \( 2m \) by each term in \( (-3m^2 + 2m + 1) \): - \( 2m \cdot (-3m^2) = -6m^3 \) - \( 2m \cdot (2m) = 4m^2 \) - \( 2m \cdot (1) = 2m \) 2. Multiply \( -1 \) by each term in \( (-3m^2 + 2m + 1) \): - \( -1 \cdot (-3m^2) = 3m^2 \) - \( -1 \cdot (2m) = -2m \) - \( -1 \cdot (1) = -1 \) Now we combine all the terms: \[ -6m^3 + 4m^2 + 2m + 3m^2 - 2m - 1 \] Next, we combine like terms: - The \( m^2 \) terms: \( 4m^2 + 3m^2 = 7m^2 \) - The \( m \) terms: \( 2m - 2m = 0 \) Putting it all together, we get: \[ -6m^3 + 7m^2 - 1 \] So the simplified product is: \[ \boxed{-6m^3 + 7m^2 - 1} \]