Whakaoti i te 6a^2+2a=

$$6 a ^ { 2 } + 2 a =$$

Tauwehe

$$2a\left(3a+1\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

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

$$a\left(3a+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2a\left(3a+1\right)$$

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.

$$6a^{2}+2a=0$$

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.

$$a=\frac{-2±\sqrt{2^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te 2^{2}.

$$a=\frac{-2±2}{2\times 6}$$

Whakareatia 2 ki te 6.

$$a=\frac{-2±2}{12}$$

Nā, me whakaoti te whārite a=\frac{-2±2}{12} ina he tāpiri te ±. Tāpiri -2 ki te 2.

$$a=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$a=0$$

Nā, me whakaoti te whārite a=\frac{-2±2}{12} ina he tango te ±. Tango 2 mai i -2.

$$a=-\frac{4}{12}$$

Whakahekea te hautanga \frac{-4}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$a=-\frac{1}{3}$$

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{1}{3} mō te x_{2}.

$$6a^{2}+2a=6a\left(a-\left(-\frac{1}{3}\right)\right)$$

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

$$6a^{2}+2a=6a\left(a+\frac{1}{3}\right)$$

Tāpiri \frac{1}{3} ki te a 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.

$$6a^{2}+2a=6a\times \frac{3a+1}{3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 6 me te 3.

$$6a^{2}+2a=2a\left(3a+1\right)$$

Aromātai

$$2a\left(3a+1\right)$$