-2а²+24аб-72б²

To simplify the expression \(-2a^2 + 24ab - 72b^2\), we can factor out the common factor. First, we notice that \(-2\) is a common factor of all terms in the expression. Let's factor out \(-2\): \[ -2(a^2 - 12ab + 36b^2) \] Now, we can focus on factoring the quadratic expression \(a^2 - 12ab + 36b^2\). This is a perfect square trinomial: \[ a^2 - 12ab + 36b^2 = (a - 6b)^2 \] Putting it all together, we have: \[ -2(a - 6b)^2 \] So, the fully factored form of the original expression \(-2a^2 + 24ab - 72b^2\) is: \[ -2(a - 6b)^2 \]