Given expression: [tex]g^3h-343h^4[/tex]
First we would factor out gcf.
GCF is h there.
Factoring out h, we get
[tex]h(g^3-343h^3)[/tex]
[tex]\mathrm{Rewrite\:}343\mathrm{\:as\:}7^3[/tex]
[tex]7^3h^3=\left(7h\right)^3[/tex]
Therefore,
[tex]g^3-343h^3 =g^3-\left(7h\right)^3[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)[/tex]
[tex]=\left(g-7h\right)\left(g^2+7gh+7^2h^2\right)[/tex]
[tex]=\left(g-7h\right)\left(g^2+7gh+49h^2\right)[/tex]
