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Prediction: 
Explanation....
Look at the familiar product when (x+1) is multiplied by (x+1) and like terms are combined in the product:
(x+1)(x+1) = x^2 + x
+ x + 1
--------------
x^2 +2x + 1
Now look what we get when (x^2+x+1) is multiplied by (x+1):
(x^2+x+1)(x+1) = x^3 + x^2 + x
+ x^2 + x + 1
-------------------
x^3 +2x^2 +2x + 1
You should be able to see that, as more powers of x are added to the first factor, the pattern of the product will continue. So in particular
x^4+x^3+x^2+x+1)(x+1) = x^5 + x^4 + x^3 + x^2 + x
+ x^4 + x^3 + x^2 + x + 1
-------------------------------
x^5 +2x^4 +2x^3 +2x^2 +2x + 1
And so
