Whakaoti i te 15a^2+12a

$$15 a ^ { 2 } + 12 a$$

Tauwehe

$$3a\left(5a+4\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(5a^{2}+4a\right)$$

Whakaarohia te 5a^{2}+4a. Tauwehea te a.

$$a\left(5a+4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3a\left(5a+4\right)$$

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.

$$15a^{2}+12a=0$$

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.

$$a=\frac{-12±\sqrt{12^{2}}}{2\times 15}$$

Tuhia te pūtakerua o te 12^{2}.

$$a=\frac{-12±12}{2\times 15}$$

Whakareatia 2 ki te 15.

$$a=\frac{-12±12}{30}$$

Nā, me whakaoti te whārite a=\frac{-12±12}{30} ina he tāpiri te ±. Tāpiri -12 ki te 12.

$$a=\frac{0}{30}$$

Whakawehe 0 ki te 30.

$$a=0$$

Nā, me whakaoti te whārite a=\frac{-12±12}{30} ina he tango te ±. Tango 12 mai i -12.

$$a=-\frac{24}{30}$$

Whakahekea te hautanga \frac{-24}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$a=-\frac{4}{5}$$

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{4}{5} mō te x_{2}.

$$15a^{2}+12a=15a\left(a-\left(-\frac{4}{5}\right)\right)$$

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

$$15a^{2}+12a=15a\left(a+\frac{4}{5}\right)$$

Tāpiri \frac{4}{5} 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.

$$15a^{2}+12a=15a\times \frac{5a+4}{5}$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 15 me te 5.

$$15a^{2}+12a=3a\left(5a+4\right)$$

Aromātai

$$3a\left(5a+4\right)$$