Whakaoti i te 8c^6+19c^3-27

$$8 c ^ { 6 } + 19 c ^ { 3 } - 27$$

Tauwehe

$$\left(c-1\right)\left(2c+3\right)\left(4c^{2}-6c+9\right)\left(c^{2}+c+1\right)$$

Ngā Upane Otinga

Kimihia he tauwehe o te āhua kc^{m}+n, e wehea ai e kc^{m} te huatahi me te pū nui rawa 8c^{6}, e wehea hoki e n te tauwehe pūmau -27. Ko tētahi tauwehe pērā ko 8c^{3}+27. Whakatauwehea te pūrau mā te whakawehe ki tēnei tauwehe.

$$\left(8c^{3}+27\right)\left(c^{3}-1\right)$$

Whakaarohia te 8c^{3}+27. Tuhia anō te 8c^{3}+27 hei \left(2c\right)^{3}+3^{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).

$$\left(2c+3\right)\left(4c^{2}-6c+9\right)$$

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

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

Me tuhi anō te kīanga whakatauwehe katoa. Kāore i tauwehea ēnei pūrau i te mea kāhore ō rātou pūtake whakahau: c^{2}+c+1,4c^{2}-6c+9.

$$\left(c-1\right)\left(c^{2}+c+1\right)\left(2c+3\right)\left(4c^{2}-6c+9\right)$$

Aromātai

$$8c^{6}+19c^{3}-27$$