Whakaoti i te -18y^3+5y^4+9y^2

$$- 18 y ^ { 3 } + 5 y ^ { 4 } + 9 y ^ { 2 }$$

Tauwehe

$$\left(y-3\right)\left(5y-3\right)y^{2}$$

Ngā Upane Otinga

Tauwehea te y^{2}.

$$y^{2}\left(-18y+5y^{2}+9\right)$$

Whakaarohia te -18y+5y^{2}+9. Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$5y^{2}-18y+9$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5y^{2}+ay+by+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-18 ab=5\times 9=45$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 45.

$$-1,-45 -3,-15 -5,-9$$

Tātaihia te tapeke mō ia takirua.

$$-1-45=-46 -3-15=-18 -5-9=-14$$

Ko te otinga te takirua ka hoatu i te tapeke -18.

$$a=-15 b=-3$$

Tuhia anō te 5y^{2}-18y+9 hei \left(5y^{2}-15y\right)+\left(-3y+9\right).

$$\left(5y^{2}-15y\right)+\left(-3y+9\right)$$

Tauwehea te 5y i te tuatahi me te -3 i te rōpū tuarua.

$$5y\left(y-3\right)-3\left(y-3\right)$$

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

$$\left(y-3\right)\left(5y-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$y^{2}\left(y-3\right)\left(5y-3\right)$$

Aromātai

$$\left(y-3\right)\left(5y-3\right)y^{2}$$