Whakaoti i te 9^6-h^6=

$$9 ^ { 6 } - h ^ { 6 } =$$

Tauwehe

$$-\left(h-9\right)\left(h+9\right)\left(h^{2}-9h+81\right)\left(h^{2}+9h+81\right)$$

Ngā Upane Otinga

Tuhia anō te 531441-h^{6} hei 729^{2}-\left(h^{3}\right)^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(729-h^{3}\right)\left(729+h^{3}\right)$$

Whakaraupapatia anō ngā kīanga tau.

$$\left(-h^{3}+729\right)\left(h^{3}+729\right)$$

Whakaarohia te -h^{3}+729. Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 729, ā, ka wehea e q te whakarea arahanga -1. Ko tetahi pūtake pērā ko 9. Tauwehea te pūrau mā te whakawehe mā te h-9.

$$\left(h-9\right)\left(-h^{2}-9h-81\right)$$

Whakaarohia te h^{3}+729. Tuhia anō te h^{3}+729 hei h^{3}+9^{3}. Ka taea te tapeke pūtoru te whakatauwehe mā te whakamahi i te ture: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(h+9\right)\left(h^{2}-9h+81\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Kāore i tauwehea ēnei pūrau i te mea kāhore ō rātou pūtake whakahau: -h^{2}-9h-81,h^{2}-9h+81.

$$\left(-h^{2}-9h-81\right)\left(h-9\right)\left(h+9\right)\left(h^{2}-9h+81\right)$$

Aromātai

$$\left(81-h^{2}\right)\left(\left(h^{2}+81\right)^{2}-81h^{2}\right)$$

Ngā Upane Otinga

Tātaihia te 9 mā te pū o 6, kia riro ko 531441.

$$531441-h^{6}$$