Whakaoti i te 125m^2-200m+80

$$125 m ^ { 2 } - 200 m + 80$$

Tauwehe

$$5\left(5m-4\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(25m^{2}-40m+16\right)$$

Whakaarohia te 25m^{2}-40m+16. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=5m, ina b=4.

$$\left(5m-4\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5\left(5m-4\right)^{2}$$

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(125m^{2}-200m+80)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(125,-200,80)=5$$

Tauwehea te 5.

$$5\left(25m^{2}-40m+16\right)$$

Kimihia te pūtakerua o te kīanga tau ārahi, 25m^{2}.

$$\sqrt{25m^{2}}=5m$$

Kimihia te pūtakerua o te kīanga tau autō, 16.

$$\sqrt{16}=4$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

$$5\left(5m-4\right)^{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$125m^{2}-200m+80=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$m=\frac{-\left(-200\right)±\sqrt{\left(-200\right)^{2}-4\times 125\times 80}}{2\times 125}$$

Pūrua -200.

$$m=\frac{-\left(-200\right)±\sqrt{40000-4\times 125\times 80}}{2\times 125}$$

Whakareatia -4 ki te 125.

$$m=\frac{-\left(-200\right)±\sqrt{40000-500\times 80}}{2\times 125}$$

Whakareatia -500 ki te 80.

$$m=\frac{-\left(-200\right)±\sqrt{40000-40000}}{2\times 125}$$

Tāpiri 40000 ki te -40000.

$$m=\frac{-\left(-200\right)±\sqrt{0}}{2\times 125}$$

Tuhia te pūtakerua o te 0.

$$m=\frac{-\left(-200\right)±0}{2\times 125}$$

Ko te tauaro o -200 ko 200.

$$m=\frac{200±0}{2\times 125}$$

Whakareatia 2 ki te 125.

$$m=\frac{200±0}{250}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{4}{5} mō te x_{1} me te \frac{4}{5} mō te x_{2}.

$$125m^{2}-200m+80=125\left(m-\frac{4}{5}\right)\left(m-\frac{4}{5}\right)$$

Tango \frac{4}{5} mai i m mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$125m^{2}-200m+80=125\times \frac{5m-4}{5}\left(m-\frac{4}{5}\right)$$

Tango \frac{4}{5} mai i m mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$125m^{2}-200m+80=125\times \frac{5m-4}{5}\times \frac{5m-4}{5}$$

Whakareatia \frac{5m-4}{5} ki te \frac{5m-4}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$125m^{2}-200m+80=125\times \frac{\left(5m-4\right)\left(5m-4\right)}{5\times 5}$$

Whakareatia 5 ki te 5.

$$125m^{2}-200m+80=125\times \frac{\left(5m-4\right)\left(5m-4\right)}{25}$$

Whakakorea atu te tauwehe pūnoa nui rawa 25 i roto i te 125 me te 25.

$$125m^{2}-200m+80=5\left(5m-4\right)\left(5m-4\right)$$

Aromātai

$$5\left(5m-4\right)^{2}$$