Simplify: 2(3x-1)² - 3(2x+1)² Expression with Squared Binomials

To solve the expression $2(3x-1)^2 - 3(2x+1)^2$, we perform these steps:

• First, expand and simplify $(3x-1)^2$:
  $(3x-1)^2 = (3x)^2 - 2(3x)(1) + 1^2 = 9x^2 - 6x + 1$.
• Next, expand and simplify $(2x+1)^2$:
  $(2x+1)^2 = (2x)^2 + 2(2x)(1) + 1^2 = 4x^2 + 4x + 1$.
• Now, multiply these by their corresponding coefficients and subtract:
  $2(3x-1)^2 = 2(9x^2 - 6x + 1) = 18x^2 - 12x + 2$,
  $3(2x+1)^2 = 3(4x^2 + 4x + 1) = 12x^2 + 12x + 3$.
• Subtract the second expression from the first:
  $18x^2 - 12x + 2 - (12x^2 + 12x + 3) = 18x^2 - 12x + 2 - 12x^2 - 12x - 3$.
• Simplify the expression:
  $6x^2 - 24x - 1$ is obtained by combining like terms.
• The final expression simplifies to $6x(x-4) - 1$ by factoring out $6x$.

The correct answer is $\mathbf{6x(x-4)-1}$, which corresponds to choice 3.