# Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises - Page 330: 63

$(2-3y)(4-3y^3)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $8+9y^4-6y^3-12y ,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Grouping the first and fourth terms and the second and third terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (8-12y)+(9y^4-6y^3) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 4(2-3y)+3y^3(3y-2) \\\\= 4(2-3y)-3y^3(2-3y) .\end{array} Factoring the $GCF= (2-3y)$ of the entire expression above results to \begin{array}{l}\require{cancel} (2-3y)(4-3y^3) .\end{array}

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.