Whakaoti i te 600-30x-40x+2x^2

$$600 - 30 x - 40 x + 2 x ^ { 2 }$$

Tauwehe

$$2\left(x-20\right)\left(x-15\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(300-15x-20x+x^{2}\right)$$

Whakaarohia te 300-15x-20x+x^{2}. Whakarea ka paheko i ngā kīanga tau ōrite.

$$x^{2}-35x+300$$

Whakaarohia te x^{2}-35x+300. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+300. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-35 ab=1\times 300=300$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 300.

$$-1,-300 -2,-150 -3,-100 -4,-75 -5,-60 -6,-50 -10,-30 -12,-25 -15,-20$$

Tātaihia te tapeke mō ia takirua.

$$-1-300=-301 -2-150=-152 -3-100=-103 -4-75=-79 -5-60=-65 -6-50=-56 -10-30=-40 -12-25=-37 -15-20=-35$$

Ko te otinga te takirua ka hoatu i te tapeke -35.

$$a=-20 b=-15$$

Tuhia anō te x^{2}-35x+300 hei \left(x^{2}-20x\right)+\left(-15x+300\right).

$$\left(x^{2}-20x\right)+\left(-15x+300\right)$$

Tauwehea te x i te tuatahi me te -15 i te rōpū tuarua.

$$x\left(x-20\right)-15\left(x-20\right)$$

Whakatauwehea atu te kīanga pātahi x-20 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-20\right)\left(x-15\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-20\right)\left(x-15\right)$$

Aromātai

$$2\left(x-20\right)\left(x-15\right)$$

Ngā Upane Otinga

Pahekotia te -30x me -40x, ka -70x.

$$600-70x+2x^{2}$$