Question

What is the answer to g3h−343h4 in algebra 2

Answer 1

Given expression:
`g^3h-343h^4`

First we would factor out gcf.

GCF is h there.

Factoring out h, we get

`h(g^3-343h^3)`

`\mathrm{Rewrite\:}343\mathrm{\:as\:}7^3`

`7^3h^3=\left(7h\right)^3`

Therefore,

`g^3-343h^3 =g^3-\left(7h\right)^3`

`\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)`

`=\left(g-7h\right)\left(g^2+7gh+7^2h^2\right)`

`=\left(g-7h\right)\left(g^2+7gh+49h^2\right)`