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

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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)

User Nilay Singh
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