Factor. \( 0.36 \mathrm{~b}^{2}-0.49 \mathrm{f}^{2} \) \( 0.36 \mathrm{~b}^{2}-0.49 \mathrm{f}^{2}=\square \)

Did you know that the expression \( 0.36 \mathrm{~b}^{2}-0.49 \mathrm{f}^{2} \) is a classic example of the difference of squares? This algebraic identity, \( a^2 - b^2 = (a - b)(a + b) \), applies here. You can rewrite \( 0.36 \) as \( (0.6b)^2 \) and \( 0.49 \) as \( (0.7f)^2 \). So, it's factored as \( (0.6b - 0.7f)(0.6b + 0.7f) \). In practice, recognizing patterns like the difference of squares can simplify problems in mathematics, physics, or even engineering. When dealing with quadratic equations, factoring can reveal solutions more easily than other methods. Just think about how this technique can save you time in your homework or during a test—it's like having a secret shortcut that gets you to the finish line faster and with less headache!