Whakaoti i te 16x^8/625-256y^4/81

$$\frac{ 16 { x }^{ 8 } }{ 625 } - \frac{ 256 { y }^{ 4 } }{ 81 }$$

Tauwehe

$$\frac{16\left(3x^{2}-10y\right)\left(3x^{2}+10y\right)\left(9x^{4}+100y^{2}\right)}{50625}$$

Ngā Upane Otinga

Tauwehea te \frac{16}{50625}.

$$\frac{16\left(81x^{8}-10000y^{4}\right)}{50625}$$

Whakaarohia te 81x^{8}-10000y^{4}. Tuhia anō te 81x^{8}-10000y^{4} hei \left(9x^{4}\right)^{2}-\left(100y^{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).

$$\left(9x^{4}-100y^{2}\right)\left(9x^{4}+100y^{2}\right)$$

Whakaarohia te 9x^{4}-100y^{2}. Tuhia anō te 9x^{4}-100y^{2} hei \left(3x^{2}\right)^{2}-\left(10y\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).

$$\left(3x^{2}-10y\right)\left(3x^{2}+10y\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\frac{16\left(3x^{2}-10y\right)\left(3x^{2}+10y\right)\left(9x^{4}+100y^{2}\right)}{50625}$$

Aromātai

$$\frac{16x^{8}}{625}-\frac{256y^{4}}{81}$$

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 625 me 81 ko 50625. Whakareatia \frac{16x^{8}}{625} ki te \frac{81}{81}. Whakareatia \frac{256y^{4}}{81} ki te \frac{625}{625}.

$$\frac{81\times 16x^{8}}{50625}-\frac{625\times 256y^{4}}{50625}$$

Tā te mea he rite te tauraro o \frac{81\times 16x^{8}}{50625} me \frac{625\times 256y^{4}}{50625}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{81\times 16x^{8}-625\times 256y^{4}}{50625}$$

Mahia ngā whakarea i roto o 81\times 16x^{8}-625\times 256y^{4}.

$$\frac{1296x^{8}-160000y^{4}}{50625}$$