Whakaoti i te 4t^2+12t

$$4 t ^ { 2 } + 12 t$$

Tauwehe

$$4t\left(t+3\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(t^{2}+3t\right)$$

Whakaarohia te t^{2}+3t. Tauwehea te t.

$$t\left(t+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4t\left(t+3\right)$$

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.

$$4t^{2}+12t=0$$

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.

$$t=\frac{-12±\sqrt{12^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te 12^{2}.

$$t=\frac{-12±12}{2\times 4}$$

Whakareatia 2 ki te 4.

$$t=\frac{-12±12}{8}$$

Nā, me whakaoti te whārite t=\frac{-12±12}{8} ina he tāpiri te ±. Tāpiri -12 ki te 12.

$$t=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-12±12}{8} ina he tango te ±. Tango 12 mai i -12.

$$t=-\frac{24}{8}$$

Whakawehe -24 ki te 8.

$$t=-3$$

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 0 mō te x_{1} me te -3 mō te x_{2}.

$$4t^{2}+12t=4t\left(t-\left(-3\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$4t^{2}+12t=4t\left(t+3\right)$$

Aromātai

$$4t\left(t+3\right)$$