Expand $(2x - 3)^{2}$.

Apply the identity $(a - b)^{2} = a^{2} - 2ab + b^{2}$ with $a = 2x$, $b = 3$: $(2x - 3)^{2} = (2x)^{2} - 2(2x)(3) + 3^{2} = 4x^{2} - 12x + 9$. - Trap A ($4x^{2} - 9$) is the *difference of squares* $(a - b)(a + b)$, not the *square of a difference* $(a - b)^{2}$. - Trap B ($4x^{2} - 6x + 9$) misses the factor of $2$ in the cross term — common when forgetting to include the $2$ in $-2ab$. - Trap D ($+12x$) gets the sign of the cross term wrong (would be $(2x + 3)^{2}$). Load-bearing detail: the middle term is $-2ab$, with both the $2$ and the negative sign from the original.