Question 1209802
Let's simplify the expression A + B.

Given:

* A = x^4 + x^3 + x^2 + x + 1
* B = x^4 - x^3 + x^2 - x + 1

We want to find A + B.

A + B = (x^4 + x^3 + x^2 + x + 1) + (x^4 - x^3 + x^2 - x + 1)

Now, combine like terms:

* x^4 + x^4 = 2x^4
* x^3 - x^3 = 0
* x^2 + x^2 = 2x^2
* x - x = 0
* 1 + 1 = 2

So, A + B = 2x^4 + 0x^3 + 2x^2 + 0x + 2

Therefore, A + B = 2x^4 + 2x^2 + 2

We can also factor out a 2:

A + B = 2(x^4 + x^2 + 1)

**Final Answer:** A + B = 2x^4 + 2x^2 + 2 or 2(x^4 + x^2 + 1)