Whakaoti i te -3a^2b+12ab-12b

$$- 3 a ^ { 2 } b + 12 a b - 12 b$$

Tauwehe

$$-3b\left(2-a\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(-a^{2}b+4ab-4b\right)$$

Whakaarohia te -a^{2}b+4ab-4b. Tauwehea te b.

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

Whakaarohia te -a^{2}+4a-4. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -a^{2}+pa+qa-4. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=4 pq=-\left(-4\right)=4$$

I te mea kua tōrunga te pq, he ōrite te tohu o p me q. I te mea kua tōrunga te p+q, he tōrunga hoki a p me q. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 4.

$$1,4 2,2$$

Tātaihia te tapeke mō ia takirua.

$$1+4=5 2+2=4$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$p=2 q=2$$

Tuhia anō te -a^{2}+4a-4 hei \left(-a^{2}+2a\right)+\left(2a-4\right).

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

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

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

Whakatauwehea atu te kīanga pātahi a-2 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$3b\left(a-2\right)\left(-a+2\right)$$

Aromātai

$$-3b\left(2-a\right)^{2}$$