Simplify the following expression:$$\frac{5.32 imes 5.32 - 3.64 imes 3.64}{1.68}$$

Question

Simplify the following expression:$$\frac{5.32 	imes 5.32 - 3.64 	imes 3.64}{1.68}$$

Examoogle · Accepted Answer

The correct answer is Option B: 8.96. Recognize the numerator as a difference of squares $a^2 - b^2$ where $a=5.32$ and $b=3.64$. Since $a-b = 5.32 - 3.64 = 1.68$, the expression simplifies instantly to $a+b = 5.32 + 3.64 = 8.96$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Recognize the numerator as a difference of squares $a^2 - b^2$ where $a=5.32$ and $b=3.64$. Since $a-b = 5.32 - 3.64 = 1.68$, the expression simplifies instantly to $a+b = 5.32 + 3.64 = 8.96$.

Formula Used: $$a^2 - b^2 = (a - b)(a + b)$$

Given: Expression to simplify: (5.32 × 5.32 - 3.64 × 3.64) / 1.68

Steps: Identify the algebraic form: The numerator is in the form $a^2 - b^2$, where $a = 5.32$ and $b = 3.64$.. Apply algebraic identity: Using the formula $a^2 - b^2 = (a - b)(a + b)$, rewrite the numerator.. Simplify and divide: Calculate the difference $5.32 - 3.64 = 1.68$. The expression becomes $\frac{1.68 	imes (5.32 + 3.64)}{1.68}$. The $1.68$ terms cancel out.

Answer: B is correct because the result of the simplification $5.32 + 3.64$ equals $8.96$.

Exam Tip: This type of simplification is common in 'Quantitative Aptitude' to test recognition of algebraic identities instead of rote computation; always look for patterns like $a^2-b^2$ or $a^2+2ab+b^2$ first.

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