Whakaoti i te (3a-2b)(3a+2b)(9a^{2}+4b^2)-(-3a)^4+(-3b^2)^2

$$( 3 a - 2 b ) ( 3 a + 2 b ) ( 9 a ^ { 2 } + 4 b ^ { 2 } ) - ( - 3 a ) ^ { 4 } + ( - 3 b ^ { 2 } ) ^ { 2 }$$

Aromātai

$$-7b^{4}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te 3a-2b ki te 3a+2b ka whakakotahi i ngā kupu rite.

$$\left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\right)-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakaarohia te \left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\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}.

$$\left(9a^{2}\right)^{2}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(9a^{2}\right)^{2}.

$$9^{2}\left(a^{2}\right)^{2}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$9^{2}a^{4}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$81a^{4}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$81a^{4}-4^{2}\left(b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$81a^{4}-4^{2}b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$81a^{4}-16b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(-3a\right)^{4}.

$$81a^{4}-16b^{4}-\left(-3\right)^{4}a^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te -3 mā te pū o 4, kia riro ko 81.

$$81a^{4}-16b^{4}-81a^{4}+\left(-3b^{2}\right)^{2}$$

Pahekotia te 81a^{4} me -81a^{4}, ka 0.

$$-16b^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(-3b^{2}\right)^{2}.

$$-16b^{4}+\left(-3\right)^{2}\left(b^{2}\right)^{2}$$

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

$$-16b^{4}+\left(-3\right)^{2}b^{4}$$

Tātaihia te -3 mā te pū o 2, kia riro ko 9.

$$-16b^{4}+9b^{4}$$

Pahekotia te -16b^{4} me 9b^{4}, ka -7b^{4}.

$$-7b^{4}$$

Whakaroha

$$-7b^{4}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te 3a-2b ki te 3a+2b ka whakakotahi i ngā kupu rite.

$$\left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\right)-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakaarohia te \left(9a^{2}-4b^{2}\right)\left(9a^{2}+4b^{2}\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}.

$$\left(9a^{2}\right)^{2}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(9a^{2}\right)^{2}.

$$9^{2}\left(a^{2}\right)^{2}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$9^{2}a^{4}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$81a^{4}-\left(4b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$81a^{4}-4^{2}\left(b^{2}\right)^{2}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

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

$$81a^{4}-4^{2}b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$81a^{4}-16b^{4}-\left(-3a\right)^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(-3a\right)^{4}.

$$81a^{4}-16b^{4}-\left(-3\right)^{4}a^{4}+\left(-3b^{2}\right)^{2}$$

Tātaihia te -3 mā te pū o 4, kia riro ko 81.

$$81a^{4}-16b^{4}-81a^{4}+\left(-3b^{2}\right)^{2}$$

Pahekotia te 81a^{4} me -81a^{4}, ka 0.

$$-16b^{4}+\left(-3b^{2}\right)^{2}$$

Whakarohaina te \left(-3b^{2}\right)^{2}.

$$-16b^{4}+\left(-3\right)^{2}\left(b^{2}\right)^{2}$$

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

$$-16b^{4}+\left(-3\right)^{2}b^{4}$$

Tātaihia te -3 mā te pū o 2, kia riro ko 9.

$$-16b^{4}+9b^{4}$$

Pahekotia te -16b^{4} me 9b^{4}, ka -7b^{4}.

$$-7b^{4}$$