## College Algebra (11th Edition)

$y^6-18y^2+8y$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $2(3y^6-9y^2+2y)-(5y^6-4y) ,$ use the Distributive Property and then combine like terms. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2(3y^6)+2(-9y^2)+2(2y)-1(5y^6)-1(-4y) \\\\= 6y^6-18y^2+4y-5y^6+4y .\end{array} By combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} (6y^6-5y^6)-18y^2+(4y+4y) \\\\= y^6-18y^2+8y .\end{array}