Whakaoti i te (x+y)(x-y)(x^{2}+y^{2})+x^{2}(y^{2}-x^2)-y^2(x^2+y^2)

$$( x + y ) ( x - y ) ( x ^ { 2 } + y ^ { 2 } ) + x ^ { 2 } ( y ^ { 2 } - x ^ { 2 } ) - y ^ { 2 } ( x ^ { 2 } + y ^ { 2 } )$$

Aromātai

$$-2y^{4}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te x+y ki te x-y ka whakakotahi i ngā kupu rite.

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

Whakaarohia te \left(x^{2}-y^{2}\right)\left(x^{2}+y^{2}\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}.

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

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

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te y^{2}-x^{2}.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te y^{2} ki te x^{2}+y^{2}.

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

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

$$-y^{4}+x^{2}y^{2}-y^{2}x^{2}-y^{4}$$

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

$$-y^{4}-y^{4}$$

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

$$-2y^{4}$$

Whakaroha

$$-2y^{4}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te x+y ki te x-y ka whakakotahi i ngā kupu rite.

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

Whakaarohia te \left(x^{2}-y^{2}\right)\left(x^{2}+y^{2}\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}.

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

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

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te y^{2}-x^{2}.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te y^{2} ki te x^{2}+y^{2}.

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

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

$$-y^{4}+x^{2}y^{2}-y^{2}x^{2}-y^{4}$$

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

$$-y^{4}-y^{4}$$

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

$$-2y^{4}$$