Whakaoti i te 3a^2-36a+108

$$3 a ^ { 2 } - 36 a + 108$$

Tauwehe

$$3\left(a-6\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(a^{2}-12a+36\right)$$

Whakaarohia te a^{2}-12a+36. Whakamahia te tikanga tātai pūrua pā, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, ina p=a, ina q=6.

$$\left(a-6\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(a-6\right)^{2}$$

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.

$$factor(3a^{2}-36a+108)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(3,-36,108)=3$$

Tauwehea te 3.

$$3\left(a^{2}-12a+36\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 36.

$$\sqrt{36}=6$$

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.

$$3\left(a-6\right)^{2}$$

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.

$$3a^{2}-36a+108=0$$

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.

$$a=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 3\times 108}}{2\times 3}$$

Pūrua -36.

$$a=\frac{-\left(-36\right)±\sqrt{1296-4\times 3\times 108}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$a=\frac{-\left(-36\right)±\sqrt{1296-12\times 108}}{2\times 3}$$

Whakareatia -12 ki te 108.

$$a=\frac{-\left(-36\right)±\sqrt{1296-1296}}{2\times 3}$$

Tāpiri 1296 ki te -1296.

$$a=\frac{-\left(-36\right)±\sqrt{0}}{2\times 3}$$

Tuhia te pūtakerua o te 0.

$$a=\frac{-\left(-36\right)±0}{2\times 3}$$

Ko te tauaro o -36 ko 36.

$$a=\frac{36±0}{2\times 3}$$

Whakareatia 2 ki te 3.

$$a=\frac{36±0}{6}$$

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 6 mō te x_{1} me te 6 mō te x_{2}.

$$3a^{2}-36a+108=3\left(a-6\right)\left(a-6\right)$$

Aromātai

$$3\left(a-6\right)^{2}$$