Whakaoti i te (5/2-r/3)(5/2+r/3)

$$( \frac { 5 } { 2 } - \frac { r } { 3 } ) ( \frac { 5 } { 2 } + \frac { r } { 3 } )$$

Aromātai

$$-\frac{r^{2}}{9}+\frac{25}{4}$$

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 2 me 3 ko 6. Whakareatia \frac{5}{2} ki te \frac{3}{3}. Whakareatia \frac{r}{3} ki te \frac{2}{2}.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

Tā te mea he rite te tauraro o \frac{5\times 3}{6} me \frac{2r}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Mahia ngā whakarea i roto o 5\times 3-2r.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 3 ko 6. Whakareatia \frac{5}{2} ki te \frac{3}{3}. Whakareatia \frac{r}{3} ki te \frac{2}{2}.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

Tā te mea he rite te tauraro o \frac{5\times 3}{6} me \frac{2r}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

Mahia ngā whakarea i roto o 5\times 3+2r.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Me whakarea te \frac{15-2r}{6} ki te \frac{15+2r}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

Whakareatia te 6 ki te 6, ka 36.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{36}$$

Whakaarohia te \left(15-2r\right)\left(15+2r\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}.

$$\frac{15^{2}-\left(2r\right)^{2}}{36}$$

Tātaihia te 15 mā te pū o 2, kia riro ko 225.

$$\frac{225-\left(2r\right)^{2}}{36}$$

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

$$\frac{225-2^{2}r^{2}}{36}$$

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

$$\frac{225-4r^{2}}{36}$$

Whakaroha

$$-\frac{r^{2}}{9}+\frac{25}{4}$$

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 2 me 3 ko 6. Whakareatia \frac{5}{2} ki te \frac{3}{3}. Whakareatia \frac{r}{3} ki te \frac{2}{2}.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

Tā te mea he rite te tauraro o \frac{5\times 3}{6} me \frac{2r}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Mahia ngā whakarea i roto o 5\times 3-2r.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 3 ko 6. Whakareatia \frac{5}{2} ki te \frac{3}{3}. Whakareatia \frac{r}{3} ki te \frac{2}{2}.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

Tā te mea he rite te tauraro o \frac{5\times 3}{6} me \frac{2r}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

Mahia ngā whakarea i roto o 5\times 3+2r.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Me whakarea te \frac{15-2r}{6} ki te \frac{15+2r}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

Whakareatia te 6 ki te 6, ka 36.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{36}$$

Whakaarohia te \left(15-2r\right)\left(15+2r\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}.

$$\frac{15^{2}-\left(2r\right)^{2}}{36}$$

Tātaihia te 15 mā te pū o 2, kia riro ko 225.

$$\frac{225-\left(2r\right)^{2}}{36}$$

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

$$\frac{225-2^{2}r^{2}}{36}$$

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

$$\frac{225-4r^{2}}{36}$$