Question 1209800
To simplify the expression (x^4 + x^3 + x^2 + x + 1) + (x^4 - x^3 + x^2 - x + 1), we combine like terms:

1. **Combine the x^4 terms:**
   x^4 + x^4 = 2x^4

2. **Combine the x^3 terms:**
   x^3 - x^3 = 0

3. **Combine the x^2 terms:**
   x^2 + x^2 = 2x^2

4. **Combine the x terms:**
   x - x = 0

5. **Combine the constant terms:**
   1 + 1 = 2

Now, put the simplified terms together:

2x^4 + 0 + 2x^2 + 0 + 2 = 2x^4 + 2x^2 + 2

Therefore, the simplified expression is 2x^4 + 2x^2 + 2.