Question : Simplify the given expression. $\frac{120 \times 120 \times 120-100 \times 100 \times 100}{120 \times 120+120 \times 100+100 \times 100}$
Option 1: 20
Option 2: 25
Option 3: 10
Option 4: 15
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Correct Answer: 20
Solution : Use identity: a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) $\frac{120 \times 120 \times 120-100 \times 100 \times 100}{120 \times 120+120 \times 100+100 \times 100}$ = $\frac{(120 -100) (120 \times 120+120 \times 100+100 \times 100)}{120 \times 120+120 \times 100+100 \times 100}$ = $20$ Hence, the correct answer is 20.
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