Whakaoti i te 175x^4+175x^3+28x^2

$$175 x ^ { 4 } + 175 x ^ { 3 } + 28 x ^ { 2 }$$

Tauwehe

$$7\left(5x+1\right)\left(5x+4\right)x^{2}$$

Ngā Upane Otinga

Tauwehea te 7.

$$7\left(25x^{4}+25x^{3}+4x^{2}\right)$$

Whakaarohia te 25x^{4}+25x^{3}+4x^{2}. Tauwehea te x^{2}.

$$x^{2}\left(25x^{2}+25x+4\right)$$

Whakaarohia te 25x^{2}+25x+4. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 25x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=25 ab=25\times 4=100$$

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 100.

$$1,100 2,50 4,25 5,20 10,10$$

Tātaihia te tapeke mō ia takirua.

$$1+100=101 2+50=52 4+25=29 5+20=25 10+10=20$$

Ko te otinga te takirua ka hoatu i te tapeke 25.

$$a=5 b=20$$

Tuhia anō te 25x^{2}+25x+4 hei \left(25x^{2}+5x\right)+\left(20x+4\right).

$$\left(25x^{2}+5x\right)+\left(20x+4\right)$$

Tauwehea te 5x i te tuatahi me te 4 i te rōpū tuarua.

$$5x\left(5x+1\right)+4\left(5x+1\right)$$

Whakatauwehea atu te kīanga pātahi 5x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(5x+1\right)\left(5x+4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$7x^{2}\left(5x+1\right)\left(5x+4\right)$$

Aromātai

$$7\left(5x+1\right)\left(5x+4\right)x^{2}$$