Whakaoti i te 12x^2-36x+27=

$$12 { x }^{ 2 } -36x+27=$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(4x^{2}-12x+9\right)$$

Whakaarohia te 4x^{2}-12x+9. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=2x, ina b=3.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

$$factor(12x^{2}-36x+27)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(12,-36,27)=3$$

Tauwehea te 3.

$$3\left(4x^{2}-12x+9\right)$$

Kimihia te pūtakerua o te kīanga tau ārahi, 4x^{2}.

$$\sqrt{4x^{2}}=2x$$

Kimihia te pūtakerua o te kīanga tau autō, 9.

$$\sqrt{9}=3$$

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.

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

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.

$$12x^{2}-36x+27=0$$

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.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 12\times 27}}{2\times 12}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 12\times 27}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{-\left(-36\right)±\sqrt{1296-48\times 27}}{2\times 12}$$

Whakareatia -48 ki te 27.

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

Tāpiri 1296 ki te -1296.

$$x=\frac{-\left(-36\right)±\sqrt{0}}{2\times 12}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-\left(-36\right)±0}{2\times 12}$$

Ko te tauaro o -36 ko 36.

$$x=\frac{36±0}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{36±0}{24}$$

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{3}{2} mō te x_{1} me te \frac{3}{2} mō te x_{2}.

$$12x^{2}-36x+27=12\left(x-\frac{3}{2}\right)\left(x-\frac{3}{2}\right)$$

Tango \frac{3}{2} mai i x 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.

$$12x^{2}-36x+27=12\times \frac{2x-3}{2}\left(x-\frac{3}{2}\right)$$

Tango \frac{3}{2} mai i x 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.

$$12x^{2}-36x+27=12\times \frac{2x-3}{2}\times \frac{2x-3}{2}$$

Whakareatia \frac{2x-3}{2} ki te \frac{2x-3}{2} 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.

$$12x^{2}-36x+27=12\times \frac{\left(2x-3\right)\left(2x-3\right)}{2\times 2}$$

Whakareatia 2 ki te 2.

$$12x^{2}-36x+27=12\times \frac{\left(2x-3\right)\left(2x-3\right)}{4}$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 12 me te 4.

$$12x^{2}-36x+27=3\left(2x-3\right)\left(2x-3\right)$$

Aromātai

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