Whakaoti i te 4m^3-32m^2+60m

$$4 m ^ { 3 } - 32 m ^ { 2 } + 60 m$$

Tauwehe

$$4m\left(m-5\right)\left(m-3\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(m^{3}-8m^{2}+15m\right)$$

Whakaarohia te m^{3}-8m^{2}+15m. Tauwehea te m.

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

Whakaarohia te m^{2}-8m+15. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm+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 m^{2}-8m+15 hei \left(m^{2}-5m\right)+\left(-3m+15\right).

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$4m\left(m-5\right)\left(m-3\right)$$

Aromātai

$$4m\left(m-5\right)\left(m-3\right)$$