Whakaoti i te x^3y^3+1-x^3-y^3=

$$x ^ { 3 } y ^ { 3 } + 1 - x ^ { 3 } - y ^ { 3 } =$$

Tauwehe

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

Ngā Upane Otinga

Mahia te whakarōpūtanga x^{3}y^{3}+1-x^{3}-y^{3}=\left(x^{3}y^{3}-x^{3}\right)+\left(-y^{3}+1\right), ka whakatauwehea atu x^{3} i te tuatahi me -1 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi y^{3}-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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 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: x^{2}+x+1,y^{2}+y+1.

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

Aromātai

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