-  Given Exp.
a2 + b2 - 2ab, where a = 186 and b = 159
= (a - b)2 = (186 - 159)2 = (27)2
= (20 + 7)2 = (20)2 + 7 + 2 x 20 x 7 = 400 + 49 + 280 = 729

To solve this problem, we can use the formula for the square of the difference of two numbers and the formula for the square of the sum of two numbers:

(a - b)² = a² - 2ab + b²

(a + b)² = a² + 2ab + b²

Using these formulas, we can simplify the given expression:

186 x 186 + 159 x 159 - 2 x 186 x 159

= (186 - 159)² + 2 x 186 x 159 (applying (a - b)² formula)

= (27)² + 2 x 186 x 159 (substituting the values of a and b)

= 729

Therefore, the correct answer is option C, which is 729.

To summarize, the given expression can be simplified using the formula for the square of the difference of two numbers and the formula for the square of the sum of two numbers. The correct value of the expression is 729, which is listed as option C.