Whakaoti i te 3m^3n-12m^2n-180mn

$$3 m ^ { 3 } n - 12 m ^ { 2 } n - 180 m n$$

Tauwehe

$$3mn\left(m-10\right)\left(m+6\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(m^{3}n-4m^{2}n-60mn\right)$$

Whakaarohia te m^{3}n-4m^{2}n-60mn. Tauwehea te mn.

$$mn\left(m^{2}-4m-60\right)$$

Whakaarohia te m^{2}-4m-60. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm-60. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=1\left(-60\right)=-60$$

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 -60.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

$$a=-10 b=6$$

Tuhia anō te m^{2}-4m-60 hei \left(m^{2}-10m\right)+\left(6m-60\right).

$$\left(m^{2}-10m\right)+\left(6m-60\right)$$

Tauwehea te m i te tuatahi me te 6 i te rōpū tuarua.

$$m\left(m-10\right)+6\left(m-10\right)$$

Whakatauwehea atu te kīanga pātahi m-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-10\right)\left(m+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3mn\left(m-10\right)\left(m+6\right)$$

Aromātai

$$3mn\left(m-10\right)\left(m+6\right)$$