Whakaoti i te (1/3+x/2)(1/9-x^2/4)(frac{1}{3}-frac{x}{2})

$$( \frac { 1 } { 3 } + \frac { x } { 2 } ) ( \frac { 1 } { 9 } - \frac { x ^ { 2 } } { 4 } ) ( \frac { 1 } { 3 } - \frac { x } { 2 } )$$

Aromātai

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

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 3 me 2 ko 6. Whakareatia \frac{1}{3} ki te \frac{2}{2}. Whakareatia \frac{x}{2} ki te \frac{3}{3}.

$$\left(\frac{2}{6}+\frac{3x}{6}\right)\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Tā te mea he rite te tauraro o \frac{2}{6} me \frac{3x}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2+3x}{6}\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 4 ko 36. Whakareatia \frac{1}{9} ki te \frac{4}{4}. Whakareatia \frac{x^{2}}{4} ki te \frac{9}{9}.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Tā te mea he rite te tauraro o \frac{4}{36} me \frac{9x^{2}}{36}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 3 me 2 ko 6. Whakareatia \frac{1}{3} ki te \frac{2}{2}. Whakareatia \frac{x}{2} ki te \frac{3}{3}.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

Tā te mea he rite te tauraro o \frac{2}{6} me \frac{3x}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Me whakarea te \frac{2+3x}{6} ki te \frac{4-9x^{2}}{36} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Me whakarea te \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} ki te \frac{2-3x}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

Whakareatia te 6 ki te 36, ka 216.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

Whakareatia te 216 ki te 6, ka 1296.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2+3x ki te 4-9x^{2}.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 8-18x^{2}+12x-27x^{3} ki te 2-3x ka whakakotahi i ngā kupu rite.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$

Whakaroha

$$\frac{x^{4}}{16}-\frac{x^{2}}{18}+\frac{1}{81}$$

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 3 me 2 ko 6. Whakareatia \frac{1}{3} ki te \frac{2}{2}. Whakareatia \frac{x}{2} ki te \frac{3}{3}.

$$\left(\frac{2}{6}+\frac{3x}{6}\right)\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Tā te mea he rite te tauraro o \frac{2}{6} me \frac{3x}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2+3x}{6}\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 4 ko 36. Whakareatia \frac{1}{9} ki te \frac{4}{4}. Whakareatia \frac{x^{2}}{4} ki te \frac{9}{9}.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Tā te mea he rite te tauraro o \frac{4}{36} me \frac{9x^{2}}{36}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 3 me 2 ko 6. Whakareatia \frac{1}{3} ki te \frac{2}{2}. Whakareatia \frac{x}{2} ki te \frac{3}{3}.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

Tā te mea he rite te tauraro o \frac{2}{6} me \frac{3x}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Me whakarea te \frac{2+3x}{6} ki te \frac{4-9x^{2}}{36} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Me whakarea te \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} ki te \frac{2-3x}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

Whakareatia te 6 ki te 36, ka 216.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

Whakareatia te 216 ki te 6, ka 1296.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2+3x ki te 4-9x^{2}.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 8-18x^{2}+12x-27x^{3} ki te 2-3x ka whakakotahi i ngā kupu rite.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$