Whakaoti i te x^5-x^3+27x^2-27=

$$x ^ { 5 } - x ^ { 3 } + 27 x ^ { 2 } - 27 =$$

Tauwehe

$$\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x^{2}-3x+9\right)$$

Ngā Upane Otinga

Mahia te whakarōpūtanga x^{5}-x^{3}+27x^{2}-27=\left(x^{5}-x^{3}\right)+\left(27x^{2}-27\right), ka whakatauwehea atu x^{3} i te tuatahi me 27 i te rōpū tuarua.

$$x^{3}\left(x^{2}-1\right)+27\left(x^{2}-1\right)$$

Whakatauwehea atu te kīanga pātahi x^{2}-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x^{2}-1\right)\left(x^{3}+27\right)$$

Whakaarohia te x^{2}-1. Tuhia anō te x^{2}-1 hei x^{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).

$$\left(x-1\right)\left(x+1\right)$$

Whakaarohia te x^{3}+27. Tuhia anō te x^{3}+27 hei x^{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).

$$\left(x+3\right)\left(x^{2}-3x+9\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Kāore te pūrau x^{2}-3x+9 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x^{2}-3x+9\right)$$

Aromātai

$$x^{5}-x^{3}+27x^{2}-27$$