Whakaoti i te -a+4a^2

$$- a + 4 a ^ { 2 }$$

Tauwehe

$$a\left(4a-1\right)$$

Ngā Upane Otinga

Tauwehea te a.

$$a\left(-1+4a\right)$$

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.

$$4a^{2}-a=0$$

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.

$$a=\frac{-\left(-1\right)±\sqrt{1}}{2\times 4}$$

Tuhia te pūtakerua o te 1.

$$a=\frac{-\left(-1\right)±1}{2\times 4}$$

Ko te tauaro o -1 ko 1.

$$a=\frac{1±1}{2\times 4}$$

Whakareatia 2 ki te 4.

$$a=\frac{1±1}{8}$$

Nā, me whakaoti te whārite a=\frac{1±1}{8} ina he tāpiri te ±. Tāpiri 1 ki te 1.

$$a=\frac{2}{8}$$

Whakahekea te hautanga \frac{2}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a=\frac{1}{4}$$

Nā, me whakaoti te whārite a=\frac{1±1}{8} ina he tango te ±. Tango 1 mai i 1.

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

Whakawehe 0 ki te 8.

$$a=0$$

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 \frac{1}{4} mō te x_{1} me te 0 mō te x_{2}.

$$4a^{2}-a=4\left(a-\frac{1}{4}\right)a$$

Tango \frac{1}{4} mai i a mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$4a^{2}-a=4\times \frac{4a-1}{4}a$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 4 me te 4.

$$4a^{2}-a=\left(4a-1\right)a$$

Aromātai

$$a\left(4a-1\right)$$