Whakaoti i te 7x-7x^7

$$7 x - 7 x ^ { 7 }$$

Tauwehe

$$7x\left(x-1\right)\left(x+1\right)\left(-x^{2}+x-1\right)\left(x^{2}+x+1\right)$$

Ngā Upane Otinga

Tauwehea te 7.

$$7\left(x-x^{7}\right)$$

Whakaarohia te x-x^{7}. Tauwehea te x.

$$x\left(1-x^{6}\right)$$

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

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

Whakaraupapatia anō ngā kīanga tau.

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

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

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

Whakaarohia te -x^{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 x-1.

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

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.

$$7x\left(x+1\right)\left(x^{2}-x+1\right)\left(x-1\right)\left(-x^{2}-x-1\right)$$

Aromātai

$$7x\left(1-x^{2}\right)\left(\left(x^{2}+1\right)^{2}-x^{2}\right)$$