Whakaoti i te 12ky^2+8ky-20k

$$12 k y ^ { 2 } + 8 k y - 20 k$$

Tauwehe

$$4k\left(y-1\right)\left(3y+5\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(3ky^{2}+2ky-5k\right)$$

Whakaarohia te 3ky^{2}+2ky-5k. Tauwehea te k.

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

Whakaarohia te 3y^{2}+2y-5. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3y^{2}+ay+by-5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=3\left(-5\right)=-15$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -15.

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

Tātaihia te tapeke mō ia takirua.

$$-1+15=14 -3+5=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-3 b=5$$

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

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

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

$$3y\left(y-1\right)+5\left(y-1\right)$$

Whakatauwehea atu te kīanga pātahi y-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y-1\right)\left(3y+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4k\left(y-1\right)\left(3y+5\right)$$

Aromātai

$$4k\left(y-1\right)\left(3y+5\right)$$