Factor: \( 36 x^{2}-49 \) (A) \( (36 x+1)(x-49) \) (B) \( (9 x-7)(4 x+7 h y \) (C) \( (6 x-7)(6 x+7) \) (D) \( (36 x-1)(36 x+1) \)

To factor \( 36 x^{2}-49 \), we recognize this as a difference of squares, which has the general form \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a^2 = 36x^2 \) (so \( a = 6x \)) and \( b^2 = 49 \) (so \( b = 7 \)). Thus, we rewrite it as follows: \[ 36 x^{2}-49 = (6x - 7)(6x + 7) \] Therefore, the correct answer is (C) \( (6 x-7)(6 x+7) \). For additional knowledge, let's delve into some interesting aspects! Factoring techniques, like recognizing the difference of squares, can make algebra both simpler and more delightful. It's like solving a mystery where finding the right pairs puts the pieces together and unveils a beautifully structured expression. When applying real-world math, such factoring is invaluable in areas such as physics and engineering. For instance, it can be used to simplify formulas when analyzing trajectories of projectiles or optimizing designs—which ultimately leads to more efficient solutions in everyday life!