Whakaoti i te -5k^3+40k^2-80k

$$- 5 k ^ { 3 } + 40 k ^ { 2 } - 80 k$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(-k^{3}+8k^{2}-16k\right)$$

Whakaarohia te -k^{3}+8k^{2}-16k. Tauwehea te k.

$$k\left(-k^{2}+8k-16\right)$$

Whakaarohia te -k^{2}+8k-16. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -k^{2}+ak+bk-16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-\left(-16\right)=16$$

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 16.

$$1,16 2,8 4,4$$

Tātaihia te tapeke mō ia takirua.

$$1+16=17 2+8=10 4+4=8$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=4 b=4$$

Tuhia anō te -k^{2}+8k-16 hei \left(-k^{2}+4k\right)+\left(4k-16\right).

$$\left(-k^{2}+4k\right)+\left(4k-16\right)$$

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

$$-k\left(k-4\right)+4\left(k-4\right)$$

Whakatauwehea atu te kīanga pātahi k-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(k-4\right)\left(-k+4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5k\left(k-4\right)\left(-k+4\right)$$

Aromātai

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