Whakaoti i te (11x+3)^2-(6x+1)(6x-1)

$$( 11 x + 3 ) ^ { 2 } - ( 6 x + 1 ) ( 6 x - 1 )$$

Aromātai

$$85x^{2}+66x+10$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(11x+3\right)^{2}.

$$121x^{2}+66x+9-\left(6x+1\right)\left(6x-1\right)$$

Whakaarohia te \left(6x+1\right)\left(6x-1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$121x^{2}+66x+9-\left(\left(6x\right)^{2}-1\right)$$

Whakarohaina te \left(6x\right)^{2}.

$$121x^{2}+66x+9-\left(6^{2}x^{2}-1\right)$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$121x^{2}+66x+9-\left(36x^{2}-1\right)$$

Hei kimi i te tauaro o 36x^{2}-1, kimihia te tauaro o ia taurangi.

$$121x^{2}+66x+9-36x^{2}+1$$

Pahekotia te 121x^{2} me -36x^{2}, ka 85x^{2}.

$$85x^{2}+66x+9+1$$

Tāpirihia te 9 ki te 1, ka 10.

$$85x^{2}+66x+10$$

Whakaroha

$$85x^{2}+66x+10$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(11x+3\right)^{2}.

$$121x^{2}+66x+9-\left(6x+1\right)\left(6x-1\right)$$

Whakaarohia te \left(6x+1\right)\left(6x-1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$121x^{2}+66x+9-\left(\left(6x\right)^{2}-1\right)$$

Whakarohaina te \left(6x\right)^{2}.

$$121x^{2}+66x+9-\left(6^{2}x^{2}-1\right)$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$121x^{2}+66x+9-\left(36x^{2}-1\right)$$

Hei kimi i te tauaro o 36x^{2}-1, kimihia te tauaro o ia taurangi.

$$121x^{2}+66x+9-36x^{2}+1$$

Pahekotia te 121x^{2} me -36x^{2}, ka 85x^{2}.

$$85x^{2}+66x+9+1$$

Tāpirihia te 9 ki te 1, ka 10.

$$85x^{2}+66x+10$$