Whakaoti i te 54x^4+27x^3a-16x-8a

$$54 x ^ { 4 } + 27 x ^ { 3 } a - 16 x - 8 a$$

Tauwehe

$$2\left(3x-2\right)\left(2x+a\right)\left(\frac{9x^{2}}{2}+3x+2\right)$$

Ngā Upane Otinga

Whakaarohia te 54x^{4}+27x^{3}a-16x-8a hei pūrau ki runga i te taurangi x.

$$54x^{4}+27ax^{3}-16x-8a$$

Kimihia he tauwehe o te āhua kx^{m}+n, e wehea ai e kx^{m} te huatahi me te pū nui rawa 54x^{4}, e wehea hoki e n te tauwehe pūmau -8a. Ko tētahi tauwehe pērā ko 6x-4. Whakatauwehea te pūrau mā te whakawehe ki tēnei tauwehe.

$$\left(6x-4\right)\left(9x^{3}+\frac{9ax^{2}}{2}+6x^{2}+3ax+4x+2a\right)$$

Whakaarohia te 6x-4. Tauwehea te 2.

$$2\left(3x-2\right)$$

Whakaarohia te 9x^{3}+\frac{9}{2}ax^{2}+6x^{2}+3ax+4x+2a. Mahia te whakarōpūtanga 9x^{3}+\frac{9ax^{2}}{2}+6x^{2}+3ax+4x+2a=\left(9x^{3}+\frac{9ax^{2}}{2}\right)+\left(6x^{2}+3ax\right)+\left(4x+2a\right), ka whakatauwehea atu \frac{9x^{2}}{2},3x,2 i tēnā rōpū, i tēnā rōpū.

$$\frac{9x^{2}}{2}\left(2x+a\right)+3x\left(2x+a\right)+2\left(2x+a\right)$$

Whakatauwehea atu te kīanga pātahi 2x+a mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x+a\right)\left(\frac{9x^{2}}{2}+3x+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa. Whakarūnātia. Kāore te pūrau 9x^{2}+6x+4 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$\left(3x-2\right)\left(9x^{2}+6x+4\right)\left(2x+a\right)$$

Aromātai

$$54x^{4}+27ax^{3}-16x-8a$$