# Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 372: 98

$\frac{x}{27}(9x+1)(81x^2-9x+1)$

#### Work Step by Step

The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$. The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$. Hence here: $27x^4+\frac{x}{27}=\\=\frac{x}{27}(729x^3+1)\\=\frac{x}{27}((9x)^3+1^3)\\=\frac{x}{27}(9x+1)((9x)^2-1(9x)+1^2)\\=\frac{x}{27}(9x+1)(81x^2-9x+1)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.