Whakaoti i te 6m^2+48m+72

$$6 m ^ { 2 } + 48 m + 72$$

Tauwehe

$$6\left(m+2\right)\left(m+6\right)$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(m^{2}+8m+12\right)$$

Whakaarohia te m^{2}+8m+12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=1\times 12=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=2 b=6$$

Tuhia anō te m^{2}+8m+12 hei \left(m^{2}+2m\right)+\left(6m+12\right).

$$\left(m^{2}+2m\right)+\left(6m+12\right)$$

Tauwehea te m i te tuatahi me te 6 i te rōpū tuarua.

$$m\left(m+2\right)+6\left(m+2\right)$$

Whakatauwehea atu te kīanga pātahi m+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m+2\right)\left(m+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6\left(m+2\right)\left(m+6\right)$$

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.

$$6m^{2}+48m+72=0$$

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.

$$m=\frac{-48±\sqrt{48^{2}-4\times 6\times 72}}{2\times 6}$$

Pūrua 48.

$$m=\frac{-48±\sqrt{2304-4\times 6\times 72}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$m=\frac{-48±\sqrt{2304-24\times 72}}{2\times 6}$$

Whakareatia -24 ki te 72.

$$m=\frac{-48±\sqrt{2304-1728}}{2\times 6}$$

Tāpiri 2304 ki te -1728.

$$m=\frac{-48±\sqrt{576}}{2\times 6}$$

Tuhia te pūtakerua o te 576.

$$m=\frac{-48±24}{2\times 6}$$

Whakareatia 2 ki te 6.

$$m=\frac{-48±24}{12}$$

Nā, me whakaoti te whārite m=\frac{-48±24}{12} ina he tāpiri te ±. Tāpiri -48 ki te 24.

$$m=-\frac{24}{12}$$

Whakawehe -24 ki te 12.

$$m=-2$$

Nā, me whakaoti te whārite m=\frac{-48±24}{12} ina he tango te ±. Tango 24 mai i -48.

$$m=-\frac{72}{12}$$

Whakawehe -72 ki te 12.

$$m=-6$$

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 -2 mō te x_{1} me te -6 mō te x_{2}.

$$6m^{2}+48m+72=6\left(m-\left(-2\right)\right)\left(m-\left(-6\right)\right)$$

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

$$6m^{2}+48m+72=6\left(m+2\right)\left(m+6\right)$$

Aromātai

$$6\left(m+2\right)\left(m+6\right)$$