SOLUTION: what is the solution to this problem,{{a^4-b^4}/{a-b}} by polynomial division.

Question 356187: what is the solution to this problem,{{a^4-b^4}/{a-b}} by polynomial division.
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
Factorization

a^4-b^4=(a^2-b^29(a^2+b^2)=(a+b)(a-b)(a^2+b^2)

Division : hence a^4-b^4 div. by a-b is (a+b)(a^2+b^2)=a^3+ab^2+a^2b+b^3

Verification by polynomial division :

a^4-b^4 | a-b
--------------
a^4-a^3b| a^3+a^2b+ab^2+b^3
---------
a^3b-b^4|
a^3b-a^2b^2
-----------
a^2b^2-b^4
a^2b^2-ab^3
------------
ab^3-b^4
ab^3-b^4
---------
0
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