Whakaoti i te 5x(x-2)-(2x+3)(2x-3)

$$5x(x-2)-(2x+3)(2x-3)$$

Aromātai

$$\left(x-9\right)\left(x-1\right)$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5x ki te x-2.

$$5x^{2}-10x-\left(2x+3\right)\left(2x-3\right)$$

Whakaarohia te \left(2x+3\right)\left(2x-3\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}.

$$5x^{2}-10x-\left(\left(2x\right)^{2}-3^{2}\right)$$

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

$$5x^{2}-10x-\left(2^{2}x^{2}-3^{2}\right)$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$5x^{2}-10x-\left(4x^{2}-3^{2}\right)$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$5x^{2}-10x-\left(4x^{2}-9\right)$$

Hei kimi i te tauaro o 4x^{2}-9, kimihia te tauaro o ia taurangi.

$$5x^{2}-10x-4x^{2}-\left(-9\right)$$

Ko te tauaro o -9 ko 9.

$$5x^{2}-10x-4x^{2}+9$$

Pahekotia te 5x^{2} me -4x^{2}, ka x^{2}.

$$x^{2}-10x+9$$

Whakaroha

$$x^{2}-10x+9$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5x ki te x-2.

$$5x^{2}-10x-\left(2x+3\right)\left(2x-3\right)$$

Whakaarohia te \left(2x+3\right)\left(2x-3\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}.

$$5x^{2}-10x-\left(\left(2x\right)^{2}-3^{2}\right)$$

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

$$5x^{2}-10x-\left(2^{2}x^{2}-3^{2}\right)$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$5x^{2}-10x-\left(4x^{2}-3^{2}\right)$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$5x^{2}-10x-\left(4x^{2}-9\right)$$

Hei kimi i te tauaro o 4x^{2}-9, kimihia te tauaro o ia taurangi.

$$5x^{2}-10x-4x^{2}-\left(-9\right)$$

Ko te tauaro o -9 ko 9.

$$5x^{2}-10x-4x^{2}+9$$

Pahekotia te 5x^{2} me -4x^{2}, ka x^{2}.

$$x^{2}-10x+9$$