Factoring a Sum or Difference of Two Cubes
Factor: 27w3 + 125y12
Step 1 Decide if the given polynomial fits a pattern.
The first term, 27w3, is a perfect cube, (3w)3.
The last term, 125y12, is a perfect cube, (5y4)3.
The terms are added.
Therefore, 27w3 + 125y12 is a sum of two cubes.
Step 2 Identify a and b. Then substitute in the pattern and simplify.
In the factoring pattern for a sum of two cubes,
substitute 3w for a and 5y4 for b.
The result is: 27w3 + 125y12 = (3w - 5y4)(9w2 - 15y4 + 25y8).
| a3 + b3
(3w)3 - (5y4)3
|= (a + b)(a2 - ab + b2)
= (3w - 5y4)[(3w)2 - 3w Â·
= (3w - 5y4)(9w2 - 15y4 + 25y8)
You can multiply to check the factorization. We leave the check to you.