Whakaoti i te (3r^2+5r-6)+(2r-5r^2)

$$( 3 r ^ { 2 } + 5 r - 6 ) + ( 2 r - 5 r ^ { 2 } )$$

Aromātai

$$\left(2-r\right)\left(2r-3\right)$$

Ngā Upane Otinga

Pahekotia te 5r me 2r, ka 7r.

$$3r^{2}+7r-6-5r^{2}$$

Pahekotia te 3r^{2} me -5r^{2}, ka -2r^{2}.

$$-2r^{2}+7r-6$$

Tauwehe

$$\left(2-r\right)\left(2r-3\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$-2r^{2}+7r-6$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -2r^{2}+ar+br-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=7 ab=-2\left(-6\right)=12$$

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 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$a=4 b=3$$

Tuhia anō te -2r^{2}+7r-6 hei \left(-2r^{2}+4r\right)+\left(3r-6\right).

$$\left(-2r^{2}+4r\right)+\left(3r-6\right)$$

Tauwehea te 2r i te tuatahi me te -3 i te rōpū tuarua.

$$2r\left(-r+2\right)-3\left(-r+2\right)$$

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

$$\left(-r+2\right)\left(2r-3\right)$$