Whakaoti i te 6x^2y-28xy+30y

$$6 x ^ { 2 } y - 28 x y + 30 y$$

Tauwehe

$$2y\left(x-3\right)\left(3x-5\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(3x^{2}y-14xy+15y\right)$$

Whakaarohia te 3x^{2}y-14xy+15y. Tauwehea te y.

$$y\left(3x^{2}-14x+15\right)$$

Whakaarohia te 3x^{2}-14x+15. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx+15. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-14 ab=3\times 15=45$$

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 -14.

$$a=-9 b=-5$$

Tuhia anō te 3x^{2}-14x+15 hei \left(3x^{2}-9x\right)+\left(-5x+15\right).

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$2y\left(x-3\right)\left(3x-5\right)$$

Aromātai

$$2y\left(x-3\right)\left(3x-5\right)$$