Whakaoti i te x^3y+6x^2y-27xy

$$x ^ { 3 } y + 6 x ^ { 2 } y - 27 x y$$

Tauwehe

$$xy\left(x-3\right)\left(x+9\right)$$

Ngā Upane Otinga

Tauwehea te xy.

$$xy\left(x^{2}+6x-27\right)$$

Whakaarohia te x^{2}+6x-27. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-27. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\left(-27\right)=-27$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -27.

$$-1,27 -3,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+27=26 -3+9=6$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=-3 b=9$$

Tuhia anō te x^{2}+6x-27 hei \left(x^{2}-3x\right)+\left(9x-27\right).

$$\left(x^{2}-3x\right)+\left(9x-27\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(x-3\right)+9\left(x-3\right)$$

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

$$\left(x-3\right)\left(x+9\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$xy\left(x-3\right)\left(x+9\right)$$

Aromātai

$$xy\left(x-3\right)\left(x+9\right)$$