Which of the following expressions is equivalent to a(b-c)-b(a+c)-c(a-b)?
Correct answer: D. -2ac
- A. bc
- B. 2ac
- C. -2bc
- D. -2ac
Explanation
To simplify the expression a(b-c)-b(a+c)-c(a-b), start by expanding each term: a(b-c) = ab - ac, -b(a+c) = -ba - bc, -c(a-b) = -ca + cb. Combining all terms results in ab - ac - ba - bc - ca + cb. Simplifying further, ab cancels out with -ba and -bc cancels out with cb, leaving -2ac. Therefore, Option D is correct. Option A is incorrect as it oversimplifies, Option B contains a sign error, and Option C focuses on the wrong terms during simplification.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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