Whakaoti i te 21m^2+21m-42

$$21 m ^ { 2 } + 21 m - 42$$

Tauwehe

$$21\left(m-1\right)\left(m+2\right)$$

Ngā Upane Otinga

Tauwehea te 21.

$$21\left(m^{2}+m-2\right)$$

Whakaarohia te m^{2}+m-2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-2\right)=-2$$

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

$$a=-1 b=2$$

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

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$21\left(m-1\right)\left(m+2\right)$$

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.

$$21m^{2}+21m-42=0$$

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.

$$m=\frac{-21±\sqrt{21^{2}-4\times 21\left(-42\right)}}{2\times 21}$$

Pūrua 21.

$$m=\frac{-21±\sqrt{441-4\times 21\left(-42\right)}}{2\times 21}$$

Whakareatia -4 ki te 21.

$$m=\frac{-21±\sqrt{441-84\left(-42\right)}}{2\times 21}$$

Whakareatia -84 ki te -42.

$$m=\frac{-21±\sqrt{441+3528}}{2\times 21}$$

Tāpiri 441 ki te 3528.

$$m=\frac{-21±\sqrt{3969}}{2\times 21}$$

Tuhia te pūtakerua o te 3969.

$$m=\frac{-21±63}{2\times 21}$$

Whakareatia 2 ki te 21.

$$m=\frac{-21±63}{42}$$

Nā, me whakaoti te whārite m=\frac{-21±63}{42} ina he tāpiri te ±. Tāpiri -21 ki te 63.

$$m=\frac{42}{42}$$

Whakawehe 42 ki te 42.

$$m=1$$

Nā, me whakaoti te whārite m=\frac{-21±63}{42} ina he tango te ±. Tango 63 mai i -21.

$$m=-\frac{84}{42}$$

Whakawehe -84 ki te 42.

$$m=-2$$

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}.

$$21m^{2}+21m-42=21\left(m-1\right)\left(m-\left(-2\right)\right)$$

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

$$21m^{2}+21m-42=21\left(m-1\right)\left(m+2\right)$$

Aromātai

$$21\left(m-1\right)\left(m+2\right)$$