Whakaoti i te left(x+7right)^2+left(-x^2-6x+7right)^2

$${ \left(x+7 \right) }^{ 2 } + { \left(- { x }^{ 2 } -6x+7 \right) }^{ 2 }$$

Aromātai

$$\left(x+7\right)^{2}\left(x^{2}-2x+2\right)$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+7\right)^{2}.

$$x^{2}+14x+49+\left(-x^{2}-6x+7\right)^{2}$$

Pūrua -x^{2}-6x+7.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)-12x\left(-x^{2}\right)-84x+\left(-x^{2}\right)^{2}+49$$

Whakareatia te -12 ki te -1, ka 12.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12xx^{2}-84x+\left(-x^{2}\right)^{2}+49$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(-x^{2}\right)^{2}+49$$

Tātaihia te -x^{2} mā te pū o 2, kia riro ko \left(x^{2}\right)^{2}.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

Pahekotia te x^{2} me 36x^{2}, ka 37x^{2}.

$$37x^{2}+14x+49+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

Pahekotia te 14x me -84x, ka -70x.

$$37x^{2}-70x+49+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}+49$$

Tāpirihia te 49 ki te 49, ka 98.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+x^{4}$$

Whakareatia te 14 ki te -1, ka -14.

$$37x^{2}-70x+98-14x^{2}+12x^{3}+x^{4}$$

Pahekotia te 37x^{2} me -14x^{2}, ka 23x^{2}.

$$23x^{2}-70x+98+12x^{3}+x^{4}$$

Whakaroha

$$x^{4}+12x^{3}+23x^{2}-70x+98$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+7\right)^{2}.

$$x^{2}+14x+49+\left(-x^{2}-6x+7\right)^{2}$$

Pūrua -x^{2}-6x+7.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)-12x\left(-x^{2}\right)-84x+\left(-x^{2}\right)^{2}+49$$

Whakareatia te -12 ki te -1, ka 12.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12xx^{2}-84x+\left(-x^{2}\right)^{2}+49$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(-x^{2}\right)^{2}+49$$

Tātaihia te -x^{2} mā te pū o 2, kia riro ko \left(x^{2}\right)^{2}.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

Pahekotia te x^{2} me 36x^{2}, ka 37x^{2}.

$$37x^{2}+14x+49+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

Pahekotia te 14x me -84x, ka -70x.

$$37x^{2}-70x+49+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}+49$$

Tāpirihia te 49 ki te 49, ka 98.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+x^{4}$$

Whakareatia te 14 ki te -1, ka -14.

$$37x^{2}-70x+98-14x^{2}+12x^{3}+x^{4}$$

Pahekotia te 37x^{2} me -14x^{2}, ka 23x^{2}.

$$23x^{2}-70x+98+12x^{3}+x^{4}$$