Whakaoti i te x^6-1

$${ x }^{ 6 } -1$$

Tauwehe

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

Ngā Upane Otinga

Tuhia anō te x^{6}-1 hei \left(x^{3}\right)^{2}-1^{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).

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

Whakaarohia te x^{3}-1. Tuhia anō te x^{3}-1 hei x^{3}-1^{3}. Ka taea te rerekētanga o ngā pūtoru te whakatauwehe mā te whakamahi i te ture: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Whakaarohia te x^{3}+1. Tuhia anō te x^{3}+1 hei x^{3}+1^{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).

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

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

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

Aromātai

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