Which expression is equivalent to 0?

Question

A. (a)(-a)
B. a + (-a)
C a/-a
D.a-(-a)

Answer 1

Let's evaluate each expression to determine which one is equivalent to 0:

A. \( (a)(-a) \)

• This equals \( -a^2 \), which is not equal to 0 unless \( a = 0 \).

B. \( a + (-a) \)

• This simplifies to \( a - a \), which is equal to 0 for any value of \( a \).

C. \( \frac{a}{-a} \)

• This simplifies to \( -1 \) for any \( a \neq 0 \) and is undefined if \( a = 0 \), so it is not equal to 0.

D. \( a - (-a) \)

• This simplifies to \( a + a = 2a \), which is not equal to 0 unless \( a = 0 \).

The only expression that is always equal to 0 (regardless of the value of \( a \)) is:

B. \( a + (-a) \)