(1) \( (2 a-5)^{2} \)

Did you know that squaring a binomial, like \( (2a-5)^2 \), follows a special pattern? This is known as the binomial square formula, which states that \( (x-y)^2 = x^2 - 2xy + y^2 \). So for our expression, it translates to \( (2a)^2 - 2 \cdot (2a) \cdot 5 + 5^2 \), ultimately resulting in \( 4a^2 - 20a + 25 \). This formula makes it a breeze to expand without getting too tangled up! Now, when using this kind of algebra in the real world, you'll often find it in areas like physics or engineering, especially in motion equations where distances relate to time squared. For instance, if you're calculating the trajectory of a projectile, you might end up encountering squared terms like these. Knowing how to manipulate binomials can be a lifesaver when it comes to tackling these practical problems!