SOLUTION: Hello and thanks in advance. I need some help with this one too; factor completely- a^4-ab^3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello and thanks in advance. I need some help with this one too; factor completely- a^4-ab^3      Log On


   

Question 174156: Hello and thanks in advance. I need some help with this one too;
factor completely- a^4-ab^3
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
a^4-ab^3
.
First, pull out what is common between both terms: a:
a(a^3-b^3)
.
Now, notice that the stuff inside the parenthesis is a "difference of cubes". This is a "special factor" condition:
http://www.purplemath.com/modules/specfact2.htm
where:
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
.
This would mean that:
a(a^3-b^3)
becomes:
a(a – b)(a^2 + ab + b^2)