Whakaoti i te 12x^2+8x

$$12 { x }^{ 2 } +8x$$

Tauwehe

$$4x\left(3x+2\right)$$

Ngā Upane Otinga

Tauwehea te 4.

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

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

$$x\left(3x+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4x\left(3x+2\right)$$

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.

$$12x^{2}+8x=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 12}$$

Tuhia te pūtakerua o te 8^{2}.

$$x=\frac{-8±8}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{-8±8}{24}$$

Nā, me whakaoti te whārite x=\frac{-8±8}{24} ina he tāpiri te ±. Tāpiri -8 ki te 8.

$$x=\frac{0}{24}$$

Whakawehe 0 ki te 24.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-8±8}{24} ina he tango te ±. Tango 8 mai i -8.

$$x=-\frac{16}{24}$$

Whakahekea te hautanga \frac{-16}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=-\frac{2}{3}$$

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 -\frac{2}{3} mō te x_{2}.

$$12x^{2}+8x=12x\left(x-\left(-\frac{2}{3}\right)\right)$$

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

$$12x^{2}+8x=12x\left(x+\frac{2}{3}\right)$$

Tāpiri \frac{2}{3} ki te x mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$12x^{2}+8x=12x\times \frac{3x+2}{3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 12 me te 3.

$$12x^{2}+8x=4x\left(3x+2\right)$$

Aromātai

$$4x\left(3x+2\right)$$