The value of $$ \frac{(0.137 + 0.098)^2 - (0.137 - 0.098)^2}{0.137 \times 0.098} $$ is

### Concept & Formula This question tests your ability to recognize the difference between two squared binomials, an extremely common pattern in aptitude tests. The key algebraic identity is: $$ (a + b)^2 - (a - b)^2 = 4ab $$ ### Step-by-Step Solution Let $a = 0.137$ and $b = 0.098$. Rewrite the given numerical expression using these variables: $$ \frac{(a + b)^2 - (a - b)^2}{a \times b} $$ Substitute the numerator with its simplified identity equivalent: $$ \frac{4ab}{ab} $$ Cancel the common term $ab$ from both the top and bottom. The remaining value is precisely $4$. ### Exam Strategy & Shortcut This is a classic "visual substitution" problem. The moment you spot the difference of squares `(a+b)^2 - (a-b)^2` sitting on top of the product `a * b`, you should instantly know the answer is $4$. You don't even need to read the actual decimals involved to select the correct option. ### Common Pitfall Students often get intimidated by the decimals and try to compute $(0.137 + 0.098)$ first, square it, and then subtract. Even if you calculate correctly, this method is too slow for competitive exams. Memorizing the $4ab$ identity is crucial. ### Final Answer **Therefore, the correct answer is 4.**