Whakaoti i te a^{2}-2a^2+3a^4-4a^5+6a^5=

$$a ^ { 2 } - 2 a ^ { 2 } + 3 a ^ { 4 } - 4 a ^ { 5 } + 6 a ^ { 5 } =$$

Aromātai

$$\left(2a-1\right)\left(a\left(a+1\right)\right)^{2}$$

Ngā Upane Otinga

Pahekotia te a^{2} me -2a^{2}, ka -a^{2}.

$$-a^{2}+3a^{4}-4a^{5}+6a^{5}$$

Pahekotia te -4a^{5} me 6a^{5}, ka 2a^{5}.

$$-a^{2}+3a^{4}+2a^{5}$$

Tauwehe

$$\left(2a-1\right)a^{2}\left(a+1\right)^{2}$$

Ngā Upane Otinga

Tauwehea te a^{2}.

$$a^{2}\left(-1+3a^{2}+2a^{3}\right)$$

Whakaarohia te 1-2+3a^{2}-4a^{3}+6a^{3}. Whakarea ka paheko i ngā kīanga tau ōrite.

$$2a^{3}+3a^{2}-1$$

Whakaarohia te 2a^{3}+3a^{2}-1. 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 -1, ā, ka wehea e q te whakarea arahanga 2. Ko tetahi pūtake pērā ko \frac{1}{2}. Tauwehea te pūrau mā te whakawehe mā te 2a-1.

$$\left(2a-1\right)\left(a^{2}+2a+1\right)$$

Whakaarohia te a^{2}+2a+1. Whakamahia te tikanga tātai pūrua pā, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, ina p=a, ina q=1.

$$\left(a+1\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$a^{2}\left(2a-1\right)\left(a+1\right)^{2}$$