Whakaoti i te 12y-2xy-2x^2y

$$12 y - 2 x y - 2 x ^ { 2 } y$$

Tauwehe

$$2y\left(2-x\right)\left(x+3\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te 6y-xy-x^{2}y. Tauwehea te y.

$$y\left(6-x-x^{2}\right)$$

Whakaarohia te 6-x-x^{2}. Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}-x+6$$

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

$$a+b=-1 ab=-6=-6$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, 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 -6.

$$1,-6 2,-3$$

Tātaihia te tapeke mō ia takirua.

$$1-6=-5 2-3=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -1.

$$a=2 b=-3$$

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

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

$$x\left(-x+2\right)+3\left(-x+2\right)$$

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

$$\left(-x+2\right)\left(x+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2y\left(-x+2\right)\left(x+3\right)$$

Aromātai

$$2y\left(2-x\right)\left(x+3\right)$$