Which of the following expressions is equivalent to a(b-c)-b(a+c)-c(a-b)?

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.