Could you explain how to factor completely
-a^3n+1 + 2b^2n+b - ab - (2a^3n*b^2n)
To factor a polynomial completely, we need to look for common factors and apply appropriate factoring methods. Let's factor the given expression -a^3n+1 + 2b^2n + b - ab - 2a^3n * b^2n step by step:
1. Group the terms together based on common factors:
-a^3n+1 - 2a^3n * b^2n + 2b^2n - ab + b
2. Look for common factors among the terms in each group:
In the first group, -a^3n+1 and -2a^3n * b^2n have a common factor of -a^3n. Factoring out -a^3n, we get: -a^3n(a^3 - 1).
In the second group, 2b^2n and b have a common factor of b. Factoring out b, we get: b(2b^n + 1).
In the last term, ab, we do not have any common factors with the other terms.
3. Combine the factored groups:
The factored expression becomes:
-a^3n(a^3 - 1) + b(2b^n + 1) - ab
So, the completely factored form of the given expression is:
-a^3n(a^3 - 1) + b(2b^n + 1) - ab