Whakaoti i te 2a^2+2a-4

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

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te a^{2}+a-2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa-2. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=1 pq=1\left(-2\right)=-2$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōrunga te p+q, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$p=-1 q=2$$

Tuhia anō te a^{2}+a-2 hei \left(a^{2}-a\right)+\left(2a-2\right).

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

Tauwehea te a i te tuatahi me te 2 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi a-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

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

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.

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

Pūrua 2.

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

Whakareatia -4 ki te 2.

$$a=\frac{-2±\sqrt{4-8\left(-4\right)}}{2\times 2}$$

Whakareatia -8 ki te -4.

$$a=\frac{-2±\sqrt{4+32}}{2\times 2}$$

Tāpiri 4 ki te 32.

$$a=\frac{-2±\sqrt{36}}{2\times 2}$$

Tuhia te pūtakerua o te 36.

$$a=\frac{-2±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$a=\frac{-2±6}{4}$$

Nā, me whakaoti te whārite a=\frac{-2±6}{4} ina he tāpiri te ±. Tāpiri -2 ki te 6.

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

Whakawehe 4 ki te 4.

$$a=1$$

Nā, me whakaoti te whārite a=\frac{-2±6}{4} ina he tango te ±. Tango 6 mai i -2.

$$a=-\frac{8}{4}$$

Whakawehe -8 ki te 4.

$$a=-2$$

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 1 mō te x_{1} me te -2 mō te x_{2}.

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

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

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

Aromātai

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