Whakaoti i te 16x^2+1/4+5x

$$16 x ^ { 2 } + \frac { 1 } { 4 } + 5 x$$

Tauwehe

$$\frac{\left(4x+1\right)\left(16x+1\right)}{4}$$

Ngā Upane Otinga

Tauwehea te \frac{1}{4}.

$$\frac{64x^{2}+1+20x}{4}$$

Whakaarohia te 64x^{2}+1+20x. Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$64x^{2}+20x+1$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 64x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=20 ab=64\times 1=64$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 64.

$$1,64 2,32 4,16 8,8$$

Tātaihia te tapeke mō ia takirua.

$$1+64=65 2+32=34 4+16=20 8+8=16$$

Ko te otinga te takirua ka hoatu i te tapeke 20.

$$a=4 b=16$$

Tuhia anō te 64x^{2}+20x+1 hei \left(64x^{2}+4x\right)+\left(16x+1\right).

$$\left(64x^{2}+4x\right)+\left(16x+1\right)$$

Whakatauwehea atu 4x i te 64x^{2}+4x.

$$4x\left(16x+1\right)+16x+1$$

Whakatauwehea atu te kīanga pātahi 16x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(16x+1\right)\left(4x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\frac{\left(16x+1\right)\left(4x+1\right)}{4}$$

Aromātai

$$16x^{2}+5x+\frac{1}{4}$$