Whakaoti i te -27a^2+81a-18a^3=

$$- 27 a ^ { 2 } + 81 a - 18 a ^ { 3 } =$$

Tauwehe

$$-9a\left(2a-3\right)\left(a+3\right)$$

Ngā Upane Otinga

Tauwehea te 9.

$$9\left(-3a^{2}+9a-2a^{3}\right)$$

Whakaarohia te -3a^{2}+9a-2a^{3}. Tauwehea te a.

$$a\left(-3a+9-2a^{2}\right)$$

Whakaarohia te -3a+9-2a^{2}. Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-2a^{2}-3a+9$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -2a^{2}+pa+qa+9. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-3 pq=-2\times 9=-18$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōraro te p+q, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$1,-18 2,-9 3,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-18=-17 2-9=-7 3-6=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -3.

$$p=3 q=-6$$

Tuhia anō te -2a^{2}-3a+9 hei \left(-2a^{2}+3a\right)+\left(-6a+9\right).

$$\left(-2a^{2}+3a\right)+\left(-6a+9\right)$$

Tauwehea te -a i te tuatahi me te -3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi 2a-3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$9a\left(2a-3\right)\left(-a-3\right)$$

Aromātai

$$-9a\left(2a-3\right)\left(a+3\right)$$