Answer
$y^6-18y^2+8y$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
