Whakaoti i te -2x^3+8x^2-8x

$$-2 { x }^{ 3 } +8 { x }^{ 2 } -8x$$

Tauwehe

$$-2x\left(2-x\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(-x^{3}+4x^{2}-4x\right)$$

Whakaarohia te -x^{3}+4x^{2}-4x. Tauwehea te x.

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

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

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

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 4.

$$1,4 2,2$$

Tātaihia te tapeke mō ia takirua.

$$1+4=5 2+2=4$$

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

$$a=2 b=2$$

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

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

Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.

$$-x\left(x-2\right)+2\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(-x+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2x\left(x-2\right)\left(-x+2\right)$$

Aromātai

$$-2x\left(2-x\right)^{2}$$