Chapter 5 - Polynomials and Factoring - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set - Page 338: 29

$rs(s+4)(s^2-4s+16)$

Work Step by Step

Factoring the $GCF= rs ,$ the given expression, $rs^4+64rs ,$ is equivalent to \begin{array}{l} rs(s^3+64) .\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, $rs(s^3+64) ,$ is \begin{array}{l} rs(s+4)[ (s)^2-(s)(4)+(4)^2] \\\\= rs(s+4)(s^2-4s+16) .\end{array}

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