[tex]\bold{[ \ Answer \ ]}[/tex]
[tex]\boxed{\bold{4(3n \ + \ 2)}}[/tex]
[tex]\bold{[ \ Explanation \ ]}[/tex]
- [tex]\bold{Simplify: \ \frac{8}{6n-4}\cdot \left(9n^2-4\right)}[/tex]
[tex]\bold{--------------------}[/tex]
- [tex]\bold{Rewrite}[/tex]
[tex]\bold{\frac{8}{6n-4} \ = \ \frac{4}{3n-2}}[/tex]
- [tex]\bold{Rewrite}[/tex]
[tex]\bold{\frac{4}{3n-2}\left(9n^2-4\right)}[/tex]
- [tex]\bold{Factor \ 9n^2-4: \ \left(3n+2\right)\left(3n-2\right)}[/tex]
[tex]\bold{9n^2-4}[/tex]
- [tex]\bold{Rewrite 9n^2-4 \ As \ \left(3n\right)^2-2^2}[/tex]
[tex]\bold{\left(3n+2\right)\left(3n-2\right)}[/tex]
- [tex]\bold{Apply \ Difference \ Of \ Two \ Squares \ Formula: \ \left(3n\right)^2-2^2=\left(3n+2\right)\left(3n-2\right)}[/tex]
[tex]\bold{\left(3n+2\right)\left(3n-2\right)}[/tex]
- [tex]\bold{Rewrite}[/tex]
[tex]\bold{\frac{4\left(3n+2\right)\left(3n-2\right)}{3n-2}}[/tex]
- [tex]\bold{Cancel \ Out \ Common \ Factor: \ 3n \ - \ 2}[/tex]
[tex]\bold{4\left(3n+2\right)}[/tex]
[tex]\boxed{\bold{[] \ Eclipsed \ []}}[/tex]
