Whakaoti i te p^3q^3-p^2q^2-pq+1

$$p ^ { 3 } q ^ { 3 } - p ^ { 2 } q ^ { 2 } - p q + 1$$

Tauwehe

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

Ngā Upane Otinga

Mahia te whakarōpūtanga p^{3}q^{3}-p^{2}q^{2}-pq+1=\left(p^{3}q^{3}-p^{2}q^{2}\right)+\left(-pq+1\right), ka whakatauwehea atu p^{2}q^{2} i te tuatahi me -1 i te rōpū tuarua.

$$p^{2}q^{2}\left(pq-1\right)-\left(pq-1\right)$$

Whakatauwehea atu te kīanga pātahi pq-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(pq-1\right)\left(p^{2}q^{2}-1\right)$$

Whakaarohia te p^{2}q^{2}-1. Tuhia anō te p^{2}q^{2}-1 hei \left(pq\right)^{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).

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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