Question

All of the following expressions have the same value, when x = -2 and y = 4, except _____.

-4 x^2
-2 xy
(-2)^2y
x^2y

Answer 1

To determine which expression has a different value when \( x = -2 \) and \( y = 4 \), we will evaluate each expression one by one.

1. **Expression: \(-4x^2\)**
\[
-4(-2)^2 = -4(4) = -16
\]

2. **Expression: \(-2xy\)**
\[
-2(-2)(4) = -2(-8) = 16
\]

3. **Expression: \((-2)^2y\)**
\[
(-2)^2(4) = 4(4) = 16
\]

4. **Expression: \(x^2y\)**
\[
(-2)^2(4) = 4(4) = 16
\]

Now we compare the results of each expression:

- \(-4x^2 = -16\)
- \(-2xy = 16\)
- \((-2)^2y = 16\)
- \(x^2y = 16\)

From these evaluations, we see that the only expression with a different value is \(-4x^2\), which equals \(-16\).

Thus, the answer is \(\boxed{-4x^2}\).