Whakaoti i te (1/2x^2-4x^-1)^3

$$( \frac { 1 } { 2 } x ^ { 2 } - 4 x ^ { - 1 } ) ^ { 3 }$$

Aromātai

$$\frac{\left(\frac{x^{3}-8}{x}\right)^{3}}{8}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(\frac{1}{2}x^{2}-4x^{-1}\right)^{3}.

$$\frac{1}{8}\left(x^{2}\right)^{3}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 3 kia riro ai te 6.

$$\frac{1}{8}x^{6}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

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

$$\frac{1}{8}x^{6}-3x^{4}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te -1 kia riro ai te 3.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te -1 me te 2 kia riro ai te -2.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}x^{-2}-64\left(x^{-1}\right)^{3}$$

Whakareatia te x^{2} ki te x^{-2}, ka 1.

$$\frac{1}{8}x^{6}-3x^{3}+24-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te -1 me te 3 kia riro ai te -3.

$$\frac{1}{8}x^{6}-3x^{3}+24-64x^{-3}$$

Whakaroha

$$\frac{x^{6}}{8}-3x^{3}+24-\frac{64}{x^{3}}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(\frac{1}{2}x^{2}-4x^{-1}\right)^{3}.

$$\frac{1}{8}\left(x^{2}\right)^{3}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 3 kia riro ai te 6.

$$\frac{1}{8}x^{6}-3\left(x^{2}\right)^{2}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

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

$$\frac{1}{8}x^{6}-3x^{4}x^{-1}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te -1 kia riro ai te 3.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}\left(x^{-1}\right)^{2}-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te -1 me te 2 kia riro ai te -2.

$$\frac{1}{8}x^{6}-3x^{3}+24x^{2}x^{-2}-64\left(x^{-1}\right)^{3}$$

Whakareatia te x^{2} ki te x^{-2}, ka 1.

$$\frac{1}{8}x^{6}-3x^{3}+24-64\left(x^{-1}\right)^{3}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te -1 me te 3 kia riro ai te -3.

$$\frac{1}{8}x^{6}-3x^{3}+24-64x^{-3}$$