Whakaoti i te 4b^2-16b+16=

$$4 b ^ { 2 } - 16 b + 16 =$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(b^{2}-4b+4\right)$$

Whakaarohia te b^{2}-4b+4. Whakamahia te tikanga tātai pūrua pā, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, ina p=b, ina q=2.

$$\left(b-2\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

$$factor(4b^{2}-16b+16)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(4,-16,16)=4$$

Tauwehea te 4.

$$4\left(b^{2}-4b+4\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 4.

$$\sqrt{4}=2$$

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.

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

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.

$$4b^{2}-16b+16=0$$

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.

$$b=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 4\times 16}}{2\times 4}$$

Pūrua -16.

$$b=\frac{-\left(-16\right)±\sqrt{256-4\times 4\times 16}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$b=\frac{-\left(-16\right)±\sqrt{256-16\times 16}}{2\times 4}$$

Whakareatia -16 ki te 16.

$$b=\frac{-\left(-16\right)±\sqrt{256-256}}{2\times 4}$$

Tāpiri 256 ki te -256.

$$b=\frac{-\left(-16\right)±\sqrt{0}}{2\times 4}$$

Tuhia te pūtakerua o te 0.

$$b=\frac{-\left(-16\right)±0}{2\times 4}$$

Ko te tauaro o -16 ko 16.

$$b=\frac{16±0}{2\times 4}$$

Whakareatia 2 ki te 4.

$$b=\frac{16±0}{8}$$

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 2 mō te x_{1} me te 2 mō te x_{2}.

$$4b^{2}-16b+16=4\left(b-2\right)\left(b-2\right)$$

Aromātai

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