Whakaoti i te -10m+1+25m^2

$$- 10 m + 1 + 25 m ^ { 2 }$$

Tauwehe

$$\left(5m-1\right)^{2}$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$25m^{2}-10m+1$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 25m^{2}+am+bm+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-10 ab=25\times 1=25$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 25.

$$-1,-25 -5,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-25=-26 -5-5=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$a=-5 b=-5$$

Tuhia anō te 25m^{2}-10m+1 hei \left(25m^{2}-5m\right)+\left(-5m+1\right).

$$\left(25m^{2}-5m\right)+\left(-5m+1\right)$$

Tauwehea te 5m i te tuatahi me te -1 i te rōpū tuarua.

$$5m\left(5m-1\right)-\left(5m-1\right)$$

Whakatauwehea atu te kīanga pātahi 5m-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(5m-1\right)\left(5m-1\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(5m-1\right)^{2}$$

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.

$$factor(25m^{2}-10m+1)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(25,-10,1)=1$$

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

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

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.

$$\left(5m-1\right)^{2}$$

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.

$$25m^{2}-10m+1=0$$

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.

$$m=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 25}}{2\times 25}$$

Pūrua -10.

$$m=\frac{-\left(-10\right)±\sqrt{100-4\times 25}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$m=\frac{-\left(-10\right)±\sqrt{100-100}}{2\times 25}$$

Tāpiri 100 ki te -100.

$$m=\frac{-\left(-10\right)±\sqrt{0}}{2\times 25}$$

Tuhia te pūtakerua o te 0.

$$m=\frac{-\left(-10\right)±0}{2\times 25}$$

Ko te tauaro o -10 ko 10.

$$m=\frac{10±0}{2\times 25}$$

Whakareatia 2 ki te 25.

$$m=\frac{10±0}{50}$$

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{1}{5} mō te x_{1} me te \frac{1}{5} mō te x_{2}.

$$25m^{2}-10m+1=25\left(m-\frac{1}{5}\right)\left(m-\frac{1}{5}\right)$$

Tango \frac{1}{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.

$$25m^{2}-10m+1=25\times \frac{5m-1}{5}\left(m-\frac{1}{5}\right)$$

Tango \frac{1}{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.

$$25m^{2}-10m+1=25\times \frac{5m-1}{5}\times \frac{5m-1}{5}$$

Whakareatia \frac{5m-1}{5} ki te \frac{5m-1}{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.

$$25m^{2}-10m+1=25\times \frac{\left(5m-1\right)\left(5m-1\right)}{5\times 5}$$

Whakareatia 5 ki te 5.

$$25m^{2}-10m+1=25\times \frac{\left(5m-1\right)\left(5m-1\right)}{25}$$

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

$$25m^{2}-10m+1=\left(5m-1\right)\left(5m-1\right)$$

Aromātai

$$\left(5m-1\right)^{2}$$