Whakaoti i te 27-125a^3-135a+225a^2

$$27 - 125 a ^ { 3 } - 135 a + 225 a ^ { 2 }$$

Tauwehe

$$\left(3-5a\right)^{3}$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 27, ā, ka wehea e q te whakarea arahanga -125. Ko tetahi pūtake pērā ko \frac{3}{5}. Tauwehea te pūrau mā te whakawehe mā te 5a-3.

$$\left(5a-3\right)\left(-25a^{2}+30a-9\right)$$

Whakaarohia te -25a^{2}+30a-9. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -25a^{2}+pa+qa-9. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=30 pq=-25\left(-9\right)=225$$

I te mea kua tōrunga te pq, he ōrite te tohu o p me q. I te mea kua tōrunga te p+q, he tōrunga hoki a p me q. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 225.

$$1,225 3,75 5,45 9,25 15,15$$

Tātaihia te tapeke mō ia takirua.

$$1+225=226 3+75=78 5+45=50 9+25=34 15+15=30$$

Ko te otinga te takirua ka hoatu i te tapeke 30.

$$p=15 q=15$$

Tuhia anō te -25a^{2}+30a-9 hei \left(-25a^{2}+15a\right)+\left(15a-9\right).

$$\left(-25a^{2}+15a\right)+\left(15a-9\right)$$

Tauwehea te -5a i te tuatahi me te 3 i te rōpū tuarua.

$$-5a\left(5a-3\right)+3\left(5a-3\right)$$

Whakatauwehea atu te kīanga pātahi 5a-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(5a-3\right)\left(-5a+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(-5a+3\right)\left(5a-3\right)^{2}$$

Aromātai

$$\left(3-5a\right)^{3}$$