Whakaoti i te 9x^2/49-12xydiv35+4y^2/25

$$\frac{ 9 { x }^{ 2 } }{ 49 } -12xy \div 35+ \frac{ 4 { y }^{ 2 } }{ 25 }$$

Aromātai

$$\frac{\left(15x-14y\right)^{2}}{1225}$$

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 49 me 35 ko 245. Whakareatia \frac{9x^{2}}{49} ki te \frac{5}{5}. Whakareatia \frac{12xy}{35} ki te \frac{7}{7}.

$$\frac{5\times 9x^{2}}{245}-\frac{7\times 12xy}{245}+\frac{4y^{2}}{25}$$

Tā te mea he rite te tauraro o \frac{5\times 9x^{2}}{245} me \frac{7\times 12xy}{245}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5\times 9x^{2}-7\times 12xy}{245}+\frac{4y^{2}}{25}$$

Mahia ngā whakarea i roto o 5\times 9x^{2}-7\times 12xy.

$$\frac{45x^{2}-84xy}{245}+\frac{4y^{2}}{25}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 245 me 25 ko 1225. Whakareatia \frac{45x^{2}-84xy}{245} ki te \frac{5}{5}. Whakareatia \frac{4y^{2}}{25} ki te \frac{49}{49}.

$$\frac{5\left(45x^{2}-84xy\right)}{1225}+\frac{49\times 4y^{2}}{1225}$$

Tā te mea he rite te tauraro o \frac{5\left(45x^{2}-84xy\right)}{1225} me \frac{49\times 4y^{2}}{1225}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5\left(45x^{2}-84xy\right)+49\times 4y^{2}}{1225}$$

Mahia ngā whakarea i roto o 5\left(45x^{2}-84xy\right)+49\times 4y^{2}.

$$\frac{225x^{2}-420xy+196y^{2}}{1225}$$

Tauwehe

$$\frac{\left(15x-14y\right)^{2}}{1225}$$

Ngā Upane Otinga

Tauwehea te \frac{1}{1225}.

$$\frac{225x^{2}-420xy+196y^{2}}{1225}$$

Whakaarohia te 225x^{2}-420xy+196y^{2}. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=15x, ina b=14y.

$$\left(15x-14y\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\frac{\left(15x-14y\right)^{2}}{1225}$$