Which of the following is the output of (141 x 141 x 141 - 58 x 58 x 58) /…
2025
Which of the following is the output of (141 x 141 x 141 - 58 x 58 x 58) / (141 x 141 + 141 x 58 + 58 x 58) ?
Answer: B. 83 — Step-by-Step SolutionTo solve this efficiently without doing complex multiplication, we can use the algebraic identity for the difference of two cubes.…
- A.
67
- B.
83
- C.
98
- D.
90
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Correct answer: B
Step-by-Step Solution
To solve this efficiently without doing complex multiplication, we can use the algebraic identity for the difference of two cubes.
Identify the structure: Let a = 141 and b = 58. The expression becomes: (a * a * a - b * b * b) / (a * a + a * b + b * b) Which is: (a^3 - b^3) / (a^2 + ab + b^2)
Use the Algebraic Identity: Recall that a^3 - b^3 = (a - b) * (a^2 + ab + b^2).
Simplify the expression: Substitute the identity into our fraction: [(a - b) * (a^2 + ab + b^2)] / (a^2 + ab + b^2)
The term (a^2 + ab + b^2) cancels out from the numerator and the denominator, leaving us with: (a - b)
Calculate the final value: a - b = 141 - 58 = 83.