Whakaoti i te 2abc^3+2abc^2-50abc-50ab

$$2 a b c ^ { 3 } + 2 a b c ^ { 2 } - 50 a b c - 50 a b$$

Tauwehe

$$2ab\left(c-5\right)\left(c+1\right)\left(c+5\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(abc^{3}+abc^{2}-25abc-25ab\right)$$

Whakaarohia te abc^{3}+abc^{2}-25abc-25ab. Tauwehea te ab.

$$ab\left(c^{3}+c^{2}-25c-25\right)$$

Whakaarohia te c^{3}+c^{2}-25c-25. Mahia te whakarōpūtanga c^{3}+c^{2}-25c-25=\left(c^{3}+c^{2}\right)+\left(-25c-25\right), ka whakatauwehea atu c^{2} i te tuatahi me -25 i te rōpū tuarua.

$$c^{2}\left(c+1\right)-25\left(c+1\right)$$

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

$$\left(c+1\right)\left(c^{2}-25\right)$$

Whakaarohia te c^{2}-25. Tuhia anō te c^{2}-25 hei c^{2}-5^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(c-5\right)\left(c+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2ab\left(c+1\right)\left(c-5\right)\left(c+5\right)$$

Aromātai

$$2ab\left(c+1\right)\left(c^{2}-25\right)$$