Whakaoti i te a^4-b^4+a^4b^4-1

$$a ^ { 4 } - b ^ { 4 } + a ^ { 4 } b ^ { 4 } - 1$$

Tauwehe

$$\left(a-1\right)\left(a+1\right)\left(a^{2}+1\right)\left(b^{4}+1\right)$$

Ngā Upane Otinga

Mahia te whakarōpūtanga a^{4}-b^{4}+a^{4}b^{4}-1=\left(a^{4}b^{4}+a^{4}\right)+\left(-b^{4}-1\right), ka whakatauwehea atu a^{4} i te tuatahi me -1 i te rōpū tuarua.

$$a^{4}\left(b^{4}+1\right)-\left(b^{4}+1\right)$$

Whakatauwehea atu te kīanga pātahi b^{4}+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(b^{4}+1\right)\left(a^{4}-1\right)$$

Whakaarohia te a^{4}-1. Tuhia anō te a^{4}-1 hei \left(a^{2}\right)^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Whakaarohia te a^{2}-1. Tuhia anō te a^{2}-1 hei a^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

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

$$\left(a-1\right)\left(a+1\right)\left(a^{2}+1\right)\left(b^{4}+1\right)$$

Aromātai

$$\left(a^{4}-1\right)\left(b^{4}+1\right)$$