What is the value of `x^(2) + 2xy +y^(2)` ?
I. `x+y=0`
II. `x =-y`.

Options

A. If statement (I) alone is sufficient to answer the question.
B. If statement (II) alone is sufficient to answer the question.
C. If either (I) or (II) alone is sufficient to answer the question.
D. If both statements (I) and (II) taken together are sufficient to answer the question.

Answer

C

Explanation

The expression can be factorized as
`x^(2) + 2xy + y^(2) = (x + y) (x+y)`.
Thus, statement I is sufficient to answer the question because it implies that the value of the entire expression is zero.
Statement II is also sufficient, for it implies that `x+y=0`.
Therefore, the correct answer choice is (c).