Whakaoti i te left(4m^4/25-16n^4/9right)left(4m^4/25+16n^4/9right)

$$\left( \frac{ 4 { m }^{ 4 } }{ 25 } - \frac{ 16 { n }^{ 4 } }{ 9 } \right) \left( \frac{ 4 { m }^{ 4 } }{ 25 } + \frac{ 16 { n }^{ 4 } }{ 9 } \right)$$

Aromātai

$$\frac{16m^{8}}{625}-\frac{256n^{8}}{81}$$

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 25 me 9 ko 225. Whakareatia \frac{4m^{4}}{25} ki te \frac{9}{9}. Whakareatia \frac{16n^{4}}{9} ki te \frac{25}{25}.

$$\left(\frac{9\times 4m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Tā te mea he rite te tauraro o \frac{9\times 4m^{4}}{225} me \frac{25\times 16n^{4}}{225}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{9\times 4m^{4}-25\times 16n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Mahia ngā whakarea i roto o 9\times 4m^{4}-25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 25 me 9 ko 225. Whakareatia \frac{4m^{4}}{25} ki te \frac{9}{9}. Whakareatia \frac{16n^{4}}{9} ki te \frac{25}{25}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{9\times 4m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

Tā te mea he rite te tauraro o \frac{9\times 4m^{4}}{225} me \frac{25\times 16n^{4}}{225}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{9\times 4m^{4}+25\times 16n^{4}}{225}$$

Mahia ngā whakarea i roto o 9\times 4m^{4}+25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{36m^{4}+400n^{4}}{225}$$

Me whakarea te \frac{36m^{4}-400n^{4}}{225} ki te \frac{36m^{4}+400n^{4}}{225} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{225\times 225}$$

Whakareatia te 225 ki te 225, ka 50625.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{50625}$$

Whakaarohia te \left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(36m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Whakarohaina te \left(36m^{4}\right)^{2}.

$$\frac{36^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te 2 kia riro ai te 8.

$$\frac{36^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Tātaihia te 36 mā te pū o 2, kia riro ko 1296.

$$\frac{1296m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Whakarohaina te \left(400n^{4}\right)^{2}.

$$\frac{1296m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te 2 kia riro ai te 8.

$$\frac{1296m^{8}-400^{2}n^{8}}{50625}$$

Tātaihia te 400 mā te pū o 2, kia riro ko 160000.

$$\frac{1296m^{8}-160000n^{8}}{50625}$$

Whakaroha

$$\frac{16m^{8}}{625}-\frac{256n^{8}}{81}$$

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 25 me 9 ko 225. Whakareatia \frac{4m^{4}}{25} ki te \frac{9}{9}. Whakareatia \frac{16n^{4}}{9} ki te \frac{25}{25}.

$$\left(\frac{9\times 4m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Tā te mea he rite te tauraro o \frac{9\times 4m^{4}}{225} me \frac{25\times 16n^{4}}{225}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{9\times 4m^{4}-25\times 16n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Mahia ngā whakarea i roto o 9\times 4m^{4}-25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 25 me 9 ko 225. Whakareatia \frac{4m^{4}}{25} ki te \frac{9}{9}. Whakareatia \frac{16n^{4}}{9} ki te \frac{25}{25}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{9\times 4m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

Tā te mea he rite te tauraro o \frac{9\times 4m^{4}}{225} me \frac{25\times 16n^{4}}{225}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{9\times 4m^{4}+25\times 16n^{4}}{225}$$

Mahia ngā whakarea i roto o 9\times 4m^{4}+25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{36m^{4}+400n^{4}}{225}$$

Me whakarea te \frac{36m^{4}-400n^{4}}{225} ki te \frac{36m^{4}+400n^{4}}{225} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{225\times 225}$$

Whakareatia te 225 ki te 225, ka 50625.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{50625}$$

Whakaarohia te \left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(36m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Whakarohaina te \left(36m^{4}\right)^{2}.

$$\frac{36^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te 2 kia riro ai te 8.

$$\frac{36^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Tātaihia te 36 mā te pū o 2, kia riro ko 1296.

$$\frac{1296m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Whakarohaina te \left(400n^{4}\right)^{2}.

$$\frac{1296m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te 2 kia riro ai te 8.

$$\frac{1296m^{8}-400^{2}n^{8}}{50625}$$

Tātaihia te 400 mā te pū o 2, kia riro ko 160000.

$$\frac{1296m^{8}-160000n^{8}}{50625}$$