\( \begin{array}{ll}\text { (1) }-(x+2)^{2}= & \text { () } x^{2}-6 x+9 \\ \text { (2) }-(x-3)^{2}= & \text { () } x^{2}-25 \\ \text { (3) }-(x+5) \cdot(x-5)= & \text { () } x^{2}+4 x+4\end{array} \)

To tackle these equations, let’s dive into a little algebra magic! Starting with the first equation: \( -(x+2)^{2} \). When you expand that, you get: \[ -(x^2 + 4x + 4) = -x^2 - 4x - 4 \] which doesn't equal \( x^2 - 6x + 9 \). For the second equation: \( -(x-3)^{2} \): \[ -(x^2 - 6x + 9) = -x^2 + 6x - 9 \] and this definitely doesn’t match \( x^{2} - 25 \). Now the third one: \( -(x+5)(x-5) = -(x^2 - 25) = -x^2 + 25 \), which does not equate to \( x^2 + 4x + 4 \). So, each of these equations presents something unusual; always remember, when in doubt about squaring or factoring, carefully expand and simplify! When solving algebraic expressions, a common mistake is forgetting to distribute negative signs properly. When you see a negative sign before a bracket, err on the side of caution and distribute it to every term inside the bracket. To further explore the beauty of algebra, consider practicing with equations that involve factoring and perfect squares. Check out resources like "Algebra for Dummies" or online platforms like Khan Academy, where fun videos and interactive exercises enhance your understanding of these concepts!