Whakaoti i te 20xy^2-20xy-15x

$$20x { y }^{ 2 } -20xy-15x$$

Tauwehe

$$5x\left(2y-3\right)\left(2y+1\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(4xy^{2}-4xy-3x\right)$$

Whakaarohia te 4xy^{2}-4xy-3x. Tauwehea te x.

$$x\left(4y^{2}-4y-3\right)$$

Whakaarohia te 4y^{2}-4y-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 4y^{2}+ay+by-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=4\left(-3\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

$$a=-6 b=2$$

Tuhia anō te 4y^{2}-4y-3 hei \left(4y^{2}-6y\right)+\left(2y-3\right).

$$\left(4y^{2}-6y\right)+\left(2y-3\right)$$

Whakatauwehea atu 2y i te 4y^{2}-6y.

$$2y\left(2y-3\right)+2y-3$$

Whakatauwehea atu te kīanga pātahi 2y-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2y-3\right)\left(2y+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5x\left(2y-3\right)\left(2y+1\right)$$

Aromātai

$$5x\left(2y-3\right)\left(2y+1\right)$$