c) \( (a+10)(a-10) \)

Did you know that the expression \( (a+10)(a-10) \) is a classic example of the difference of squares? This nifty algebraic identity states that when you multiply two binomials in the form of \( (x+y)(x-y) \), the result is \( x^2 - y^2 \). So in this case, \( a^2 - 100 \) is the simplified expression of \( (a+10)(a-10) \). In real-world applications, this concept pops up in various fields, including physics and engineering. For instance, when calculating the area differences in structures or when optimizing designs, using the difference of squares can simplify calculations and make problem-solving more efficient. Who knew algebra could have such practical uses, right?