Whakaoti i te v^2+3v+7v+21

$$v ^ { 2 } + 3 v + 7 v + 21$$

Tauwehe

$$\left(v+3\right)\left(v+7\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$v^{2}+10v+21$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei v^{2}+av+bv+21. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=1\times 21=21$$

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 21.

$$1,21 3,7$$

Tātaihia te tapeke mō ia takirua.

$$1+21=22 3+7=10$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$a=3 b=7$$

Tuhia anō te v^{2}+10v+21 hei \left(v^{2}+3v\right)+\left(7v+21\right).

$$\left(v^{2}+3v\right)+\left(7v+21\right)$$

Tauwehea te v i te tuatahi me te 7 i te rōpū tuarua.

$$v\left(v+3\right)+7\left(v+3\right)$$

Whakatauwehea atu te kīanga pātahi v+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(v+3\right)\left(v+7\right)$$

Aromātai

$$\left(v+3\right)\left(v+7\right)$$

Ngā Upane Otinga

Pahekotia te 3v me 7v, ka 10v.

$$v^{2}+10v+21$$