SOLUTION: First, rewrite 125q3 as (5q)3.
Then you'll have: p³ + (5q)³ or (p³) + 5³q³.
Since both terms are perfect cubes, factor using the sum of cubes formula: a³ + b³ = (a+b) (a² - ab + b²) where a=p and b=5q.
Simplify: (p + 5q) (p² − 5pq + 25q²).
Factoring polynomial expressions is not quite the same as factoring numbers, but the concept is very similar.
When factoring numbers or factoring polynomials, you are finding numbers or polynomials that divide out evenly from the original numbers or polynomials. But in the case of polynomials, you are dividing numbers and variables out of expressions, not just dividing numbers out of numbers.
The first method for factoring polynomials will be factoring out the greatest common factor. When factoring in general this will also be the first thing that we should try as it will often simplify the problem.
To use this method all that we do is look at all the terms and determine if there is a factor that is in common to all the terms. If there is, we will factor it out of the polynomial. Also note that in this case we are really only using the distributive law in reverse. Remember that the distributive law states that: a(b+c) = ab+ac.
In factoring out the greatest common factor we do this in reverse. We notice that each term has an a in it and so we “factor” it out using the distributive law in reverse as follows: ab+ac= a(b+c).
Learn more about factoring polynomials at tutorial.math.lamar.edu.