If a, b, and c are in AP, then the value of (a + 2b - c)(2b + c - a)(c + a - b) is:
Correct: D
Since a, b, c are in AP, 2b = a + c. (a + 2b - c)(2b + c - a)(c + a - b) = (a + a + c - c)(a + c + c - a)(c + a - (a+c)/2) = (2a)(2c)(2c/2+2a/2 - (a+c)/2) = (2a)(2c)((2c+2a-a-c)/2) = 4ac((a+c)/2) = 4ac(b) = 4abc. But a+c = 2b is only true, if a,b,c are in AP. It should be (a+2b-c)(2b+c-a)(c+a-b). = (2b+2b-2b)(2b)(b) = (2b)^3