Whakaoti i te y^6+7y^3-8

$$y ^ { 6 } + 7 y ^ { 3 } - 8$$

Tauwehe

$$\left(y-1\right)\left(y+2\right)\left(y^{2}-2y+4\right)\left(y^{2}+y+1\right)$$

Ngā Upane Otinga

Kimihia he tauwehe o te āhua y^{k}+m, e wehea ai e y^{k} te huatahi me te pū nui rawa y^{6}, e wehea hoki e m te tauwehe pūmau -8. Ko tētahi tauwehe pērā ko y^{3}+8. Whakatauwehea te pūrau mā te whakawehe ki tēnei tauwehe.

$$\left(y^{3}+8\right)\left(y^{3}-1\right)$$

Whakaarohia te y^{3}+8. Tuhia anō te y^{3}+8 hei y^{3}+2^{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).

$$\left(y+2\right)\left(y^{2}-2y+4\right)$$

Whakaarohia te y^{3}-1. Tuhia anō te y^{3}-1 hei y^{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).

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

Me tuhi anō te kīanga whakatauwehe katoa. Kāore i tauwehea ēnei pūrau i te mea kāhore ō rātou pūtake whakahau: y^{2}+y+1,y^{2}-2y+4.

$$\left(y-1\right)\left(y^{2}+y+1\right)\left(y+2\right)\left(y^{2}-2y+4\right)$$

Aromātai

$$y^{6}+7y^{3}-8$$