27a²b²-18ab+3

To simplify the expression \(27a^2b^2 - 18ab + 3\), we can look for a way to factor it, particularly for common factors. 1. **Identify the common factors:** The coefficients \(27\), \(-18\), and \(3\) have a greatest common divisor of \(3\). 2. **Factor out \(3\):** \[ 27a^2b^2 - 18ab + 3 = 3(9a^2b^2 - 6ab + 1) \] 3. **Now, let’s focus on factoring the quadratic \(9a^2b^2 - 6ab + 1\):** We can attempt to factor it as a perfect square trinomial. - The expression can be checked if it fits the form \((px + q)^2\). - Evaluating, we find: \((3ab - 1)^2 = 9a^2b^2 - 6ab + 1\) Thus, the complete factorization is: \[ 27a^2b^2 - 18ab + 3 = 3(3ab - 1)^2 \] You can use this result for further evaluations or calculations as needed.