# Chapter 5 - Polynomials and Factoring - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set - Page 338: 27

$2(3x+1)(9x^2-3x+1)$

#### Work Step by Step

Factoring the $GCF= 2 ,$ the given expression, $54x^3+2 ,$ is equivalent to \begin{array}{l} 2(27x^3+1) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $2(27x^3+1) ,$ is \begin{array}{l} 2(3x+1)[ (3x)^2-(3x)(1)+(1)^2] \\\\= 2(3x+1)(9x^2-3x+1) .\end{array}

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