Whakaoti i te 1-a^6

$$1 - a ^ { 6 }$$

Tauwehe

$$\left(a-1\right)\left(a+1\right)\left(-a^{2}+a-1\right)\left(a^{2}+a+1\right)$$

Ngā Upane Otinga

Tuhia anō te 1-a^{6} hei 1^{2}-\left(-a^{3}\right)^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(1+a^{3}\right)\left(1-a^{3}\right)$$

Whakaraupapatia anō ngā kīanga tau.

$$\left(a^{3}+1\right)\left(-a^{3}+1\right)$$

Whakaarohia te a^{3}+1. Tuhia anō te a^{3}+1 hei a^{3}+1^{3}. Ka taea te tapeke pūtoru te whakatauwehe mā te whakamahi i te ture: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

$$\left(a+1\right)\left(a^{2}-a+1\right)$$

Whakaarohia te -a^{3}+1. 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 1, ā, ka wehea e q te whakarea arahanga -1. Ko tetahi pūtake pērā ko 1. Tauwehea te pūrau mā te whakawehe mā te a-1.

$$\left(a-1\right)\left(-a^{2}-a-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Kāore i tauwehea ēnei pūrau i te mea kāhore ō rātou pūtake whakahau: -a^{2}-a-1,a^{2}-a+1.

$$\left(-a^{2}-a-1\right)\left(a-1\right)\left(a^{2}-a+1\right)\left(a+1\right)$$

Aromātai

$$\left(1-a^{2}\right)\left(\left(a^{2}+1\right)^{2}-a^{2}\right)$$