Whakaoti i te 48t-12t^2

$$48 t - 12 t ^ { 2 }$$

Tauwehe

$$12t\left(4-t\right)$$

Ngā Upane Otinga

Tauwehea te 12.

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

Whakaarohia te 4t-t^{2}. Tauwehea te t.

$$t\left(4-t\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$12t\left(-t+4\right)$$

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.

$$-12t^{2}+48t=0$$

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.

$$t=\frac{-48±\sqrt{48^{2}}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 48^{2}.

$$t=\frac{-48±48}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$t=\frac{-48±48}{-24}$$

Nā, me whakaoti te whārite t=\frac{-48±48}{-24} ina he tāpiri te ±. Tāpiri -48 ki te 48.

$$t=\frac{0}{-24}$$

Whakawehe 0 ki te -24.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-48±48}{-24} ina he tango te ±. Tango 48 mai i -48.

$$t=-\frac{96}{-24}$$

Whakawehe -96 ki te -24.

$$t=4$$

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 4 mō te x_{2}.

$$-12t^{2}+48t=-12t\left(t-4\right)$$

Aromātai

$$12t\left(4-t\right)$$