Question

For the given expression, which expression yields the same answer when x = 3 and y = 1?

Given: 2x + y x + 2y^2, x^2 - 2y, x^2 - y^2, 2( x + y)

Answer 1

To find which expression yields the same answer when \( x = 3 \) and \( y = 1 \), let's evaluate each expression step by step.

1. **Expression: \( 2x + y \)**
\[
= 2(3) + 1 = 6 + 1 = 7
\]

2. **Expression: \( x + 2y^2 \)**
\[
= 3 + 2(1^2) = 3 + 2(1) = 3 + 2 = 5
\]

3. **Expression: \( x^2 - 2y \)**
\[
= 3^2 - 2(1) = 9 - 2 = 7
\]

4. **Expression: \( x^2 - y^2 \)**
\[
= 3^2 - 1^2 = 9 - 1 = 8
\]

5. **Expression: \( 2(x + y) \)**
\[
= 2(3 + 1) = 2(4) = 8
\]

Now, let's summarize the results:
- \( 2x + y = 7 \)
- \( x + 2y^2 = 5 \)
- \( x^2 - 2y = 7 \)
- \( x^2 - y^2 = 8 \)
- \( 2(x + y) = 8 \)

The expressions that yield the same results when \( x = 3 \) and \( y = 1 \) are:
- \( 2x + y = 7 \)
- \( x^2 - 2y = 7 \)

Thus, the expressions \( 2x + y \) and \( x^2 - 2y \) yield the same answer, which is \( 7 \).

### Answer
\( 2x + y \) and \( x^2 - 2y \) yield the same answer (7).