Whakaoti i te 16n^3+80n^2-9n-45

$$16 n ^ { 3 } + 80 n ^ { 2 } - 9 n - 45$$

Tauwehe

$$\left(4n-3\right)\left(n+5\right)\left(4n+3\right)$$

Ngā Upane Otinga

Mahia te whakarōpūtanga 16n^{3}+80n^{2}-9n-45=\left(16n^{3}+80n^{2}\right)+\left(-9n-45\right), ka whakatauwehea atu 16n^{2} i te tuatahi me -9 i te rōpū tuarua.

$$16n^{2}\left(n+5\right)-9\left(n+5\right)$$

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

$$\left(n+5\right)\left(16n^{2}-9\right)$$

Whakaarohia te 16n^{2}-9. Tuhia anō te 16n^{2}-9 hei \left(4n\right)^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4n-3\right)\left(4n+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(4n-3\right)\left(4n+3\right)\left(n+5\right)$$

Aromātai

$$\left(n+5\right)\left(16n^{2}-9\right)$$