Whakaoti i te [(x+1)(x-1)]^2-(2+x^2)^2+3/2(2x-3)(2x+3)

$$[ ( x + 1 ) ( x - 1 ) ] ^ { 2 } - ( 2 + x ^ { 2 } ) ^ { 2 } + \frac { 3 } { 2 } ( 2 x - 3 ) ( 2 x + 3 )$$

Aromātai

$$-\frac{33}{2}=-16.5$$

Ngā Upane Otinga

Whakaarohia te \left(x+1\right)\left(x-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.

$$\left(x^{2}-1\right)^{2}-\left(2+x^{2}\right)^{2}+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x^{2}-1\right)^{2}.

$$\left(x^{2}\right)^{2}-2x^{2}+1-\left(2+x^{2}\right)^{2}+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

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

$$x^{4}-2x^{2}+1-\left(2+x^{2}\right)^{2}+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

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

$$x^{4}-2x^{2}+1-\left(4+4x^{2}+\left(x^{2}\right)^{2}\right)+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

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

$$x^{4}-2x^{2}+1-\left(4+4x^{2}+x^{4}\right)+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

Hei kimi i te tauaro o 4+4x^{2}+x^{4}, kimihia te tauaro o ia taurangi.

$$x^{4}-2x^{2}+1-4-4x^{2}-x^{4}+\frac{3}{2}\left(2x-3\right)\left(2x+3\right)$$

Tangohia te 4 i te 1, ka -3.

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

Pahekotia te -2x^{2} me -4x^{2}, ka -6x^{2}.

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

Pahekotia te x^{4} me -x^{4}, ka 0.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{2} ki te 2x-3.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-\frac{9}{2} ki te 2x+3 ka whakakotahi i ngā kupu rite.

$$-6x^{2}-3+6x^{2}-\frac{27}{2}$$

Pahekotia te -6x^{2} me 6x^{2}, ka 0.

$$-3-\frac{27}{2}$$

Tangohia te \frac{27}{2} i te -3, ka -\frac{33}{2}.

$$-\frac{33}{2}$$

Tauwehe

$$-\frac{33}{2} = -16\frac{1}{2} = -16.5$$

Ngā Upane Otinga

Tauwehea te \frac{1}{2}.

$$\frac{2\left(\left(x+1\right)\left(x-1\right)\right)^{2}-2\left(2+x^{2}\right)^{2}+3\left(2x-3\right)\left(2x+3\right)}{2}$$

Whakarūnātia.

$$-\frac{33}{2}$$