\(200^2 - 2(200)(199) + 199^2 =\)

[Gmat_mission]

\(200^2 - 2(200)(199) + 199^2 =\)

(A) \(-79,201\)
(B) \(-200\)
(C) \(1\)
(D) \(200\)
(E) \(79,999\)

Answer: C

Source: Princeton Review

[DHRJ007]

just use the property of (a+b)whole square.
(200-199)whole square =1


ans:C

[Scott@TargetTestPrep]

\(200^2 - 2(200)(199) + 199^2 =\)

(A) \(-79,201\)
(B) \(-200\)
(C) \(1\)
(D) \(200\)
(E) \(79,999\)

Answer: C

Solution:

Letting x = 200 and y = 199, we have:

x^2 - 2xy + y^2 = (x - y)^2

Therefore, the result is (200 - 199)^2 = 1^2 = 1.

Answer: C