Whakaoti i te x^4/16-y^4/81

$$\frac{ { x }^{ 4 } }{ 16 } - \frac{ { y }^{ 4 } }{ 81 }$$

Tauwehe

$$\frac{\left(3x-2y\right)\left(3x+2y\right)\left(9x^{2}+4y^{2}\right)}{1296}$$

Ngā Upane Otinga

Tauwehea te \frac{1}{1296}.

$$\frac{81x^{4}-16y^{4}}{1296}$$

Whakaarohia te 81x^{4}-16y^{4}. Tuhia anō te 81x^{4}-16y^{4} hei \left(9x^{2}\right)^{2}-\left(4y^{2}\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).

$$\left(9x^{2}-4y^{2}\right)\left(9x^{2}+4y^{2}\right)$$

Whakaarohia te 9x^{2}-4y^{2}. Tuhia anō te 9x^{2}-4y^{2} hei \left(3x\right)^{2}-\left(2y\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).

$$\left(3x-2y\right)\left(3x+2y\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\frac{\left(3x-2y\right)\left(3x+2y\right)\left(9x^{2}+4y^{2}\right)}{1296}$$

Aromātai

$$\frac{x^{4}}{16}-\frac{y^{4}}{81}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 16 me 81 ko 1296. Whakareatia \frac{x^{4}}{16} ki te \frac{81}{81}. Whakareatia \frac{y^{4}}{81} ki te \frac{16}{16}.

$$\frac{81x^{4}}{1296}-\frac{16y^{4}}{1296}$$

Tā te mea he rite te tauraro o \frac{81x^{4}}{1296} me \frac{16y^{4}}{1296}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{81x^{4}-16y^{4}}{1296}$$