Question 1209802: Let A = x^4 + x^3 + x^2 + x + 1 and B = x^4 - x^3 + x^2 - x + 1. Simplify A + B. Found 2 solutions by CPhill, greenestamps:Answer by CPhill(1987) (Show Source):
You can put this solution on YOUR website! 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)
