What would be the result of the following expression? \(\frac{{1
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What would be the result of the following expression?
\(\frac{{192 \times 192 \times 192 - 8 \times 8 \times 8}}{{192 \times 192 + 192 \times 8 + 8 \times 8}}\)
A. 200
B. 184
C. 1
D. 4
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
As we know, (a3 – b3) = (a – b) (a2 + b2 + ab)
\(\Rightarrow \frac{{192 \times 192 \times 192 - 8 \times 8 \times 8}}{{192 \times 192 + 192 \times 8 + 8 \times 8}}\)
\(\Rightarrow \frac{{{{192}^3} - {8^3}}}{{{{192}^2} + 192 \times 8 + {8^2}}}\)
\(\Rightarrow \frac{{\left( {192 - 8} \right)({{192}^2} + 192 \times 8 + {8^2})}}{{{{192}^2} + 192 \times 8 + {8^2}}}\)
⇒ (192 – 8)
⇒ 184