Whakaoti i te 5a^2b-10ab-40b

$$5 a ^ { 2 } b - 10 a b - 40 b$$

Tauwehe

$$5b\left(a-4\right)\left(a+2\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(a^{2}b-2ab-8b\right)$$

Whakaarohia te a^{2}b-2ab-8b. Tauwehea te b.

$$b\left(a^{2}-2a-8\right)$$

Whakaarohia te a^{2}-2a-8. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa-8. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-2 pq=1\left(-8\right)=-8$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōraro te p+q, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -8.

$$1,-8 2,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-8=-7 2-4=-2$$

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

$$p=-4 q=2$$

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

$$\left(a^{2}-4a\right)+\left(2a-8\right)$$

Tauwehea te a i te tuatahi me te 2 i te rōpū tuarua.

$$a\left(a-4\right)+2\left(a-4\right)$$

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

$$\left(a-4\right)\left(a+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5b\left(a-4\right)\left(a+2\right)$$

Aromātai

$$5b\left(a-4\right)\left(a+2\right)$$