Whakaoti i te 4x^3y-44x^2y+112xy

$$4 x ^ { 3 } y - 44 x ^ { 2 } y + 112 x y$$

Tauwehe

$$4xy\left(x-7\right)\left(x-4\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(x^{3}y-11x^{2}y+28xy\right)$$

Whakaarohia te x^{3}y-11x^{2}y+28xy. Tauwehea te xy.

$$xy\left(x^{2}-11x+28\right)$$

Whakaarohia te x^{2}-11x+28. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+28. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=1\times 28=28$$

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 28.

$$-1,-28 -2,-14 -4,-7$$

Tātaihia te tapeke mō ia takirua.

$$-1-28=-29 -2-14=-16 -4-7=-11$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-7 b=-4$$

Tuhia anō te x^{2}-11x+28 hei \left(x^{2}-7x\right)+\left(-4x+28\right).

$$\left(x^{2}-7x\right)+\left(-4x+28\right)$$

Tauwehea te x i te tuatahi me te -4 i te rōpū tuarua.

$$x\left(x-7\right)-4\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(x-4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4xy\left(x-7\right)\left(x-4\right)$$

Aromātai

$$4xy\left(x-7\right)\left(x-4\right)$$