Whakaoti i te y^4-8y^3+15y^2=

$$y ^ { 4 } - 8 y ^ { 3 } + 15 y ^ { 2 } =$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te y^{2}.

$$y^{2}\left(y^{2}-8y+15\right)$$

Whakaarohia te y^{2}-8y+15. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by+15. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=1\times 15=15$$

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 15.

$$-1,-15 -3,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-15=-16 -3-5=-8$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

$$a=-5 b=-3$$

Tuhia anō te y^{2}-8y+15 hei \left(y^{2}-5y\right)+\left(-3y+15\right).

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

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

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

Whakatauwehea atu te kīanga pātahi y-5 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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