Question : Simplify the given expression.
$\frac{(3.254 \times 3.254 \times 3.254)-(0.746 \times 0.746 \times 0.746)}{(3.254 \times 3.254)+(0.746 \times 0.746)+(3.254 \times 0.746)}$
Option 1: 3.156
Option 2: 4.508
Option 3: 2.146
Option 4: 2.508
Correct Answer: 2.508
Solution :
Given: $\frac{(3.254 \times 3.254 \times 3.254)-(0.746 \times 0.746 \times 0.746)}{(3.254 \times 3.254)+(0.746 \times 0.746)+(3.254 \times 0.746)}$
Let $a=3.254$ and $b=0.746$
= $\frac{a^3-b^3}{a^2+b^2+ab}$
= $\frac{(a-b)(a^2+b^2+ab)}{a^2+b^2+ab}$
= $a-b$
Putting the values, we get:
= 3.254 – 0.746
= 2.508
Hence, the correct answer is 2.508.
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