Whakaoti i te (x-y+1/2)(x-y+1/2)-(x-y)^{2}+(1/3x^{2}-3/2)^3-x^2(frac{1}{27}x^4-frac{1}{2}x^2+frac{9}{4})

$$( x - y + \frac { 1 } { 2 } ) ( x - y + \frac { 1 } { 2 } ) - ( x - y ) ^ { 2 } + ( \frac { 1 } { 3 } x ^ { 2 } - \frac { 3 } { 2 } ) ^ { 3 } - x ^ { 2 } ( \frac { 1 } { 27 } x ^ { 4 } - \frac { 1 } { 2 } x ^ { 2 } + \frac { 9 } { 4 } )$$

Aromātai

$$x-y-\frac{25}{8}$$

Ngā Upane Otinga

Whakareatia te x-y+\frac{1}{2} ki te x-y+\frac{1}{2}, ka \left(x-y+\frac{1}{2}\right)^{2}.

$$\left(x-y+\frac{1}{2}\right)^{2}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Pūrua x-y+\frac{1}{2}.

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x^{2}-2xy+y^{2}\right)+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-x^{2}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$-2xy+x+y^{2}-y+\frac{1}{4}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Pahekotia te -2xy me 2xy, ka 0.

$$x+y^{2}-y+\frac{1}{4}-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}.

$$x-y+\frac{1}{4}+\frac{1}{27}\left(x^{2}\right)^{3}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 3 kia riro ai te 6.

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Tangohia te \frac{27}{8} i te \frac{1}{4}, ka -\frac{25}{8}.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te \frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\left(\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}\right)$$

Hei kimi i te tauaro o \frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}, kimihia te tauaro o ia taurangi.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{1}{27}x^{6}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

Pahekotia te \frac{1}{27}x^{6} me -\frac{1}{27}x^{6}, ka 0.

$$x-y-\frac{25}{8}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

Pahekotia te -\frac{1}{2}x^{4} me \frac{1}{2}x^{4}, ka 0.

$$x-y-\frac{25}{8}+\frac{9}{4}x^{2}-\frac{9}{4}x^{2}$$

Pahekotia te \frac{9}{4}x^{2} me -\frac{9}{4}x^{2}, ka 0.

$$x-y-\frac{25}{8}$$

Whakaroha

$$x-y-\frac{25}{8}$$

Ngā Upane Otinga

Whakareatia te x-y+\frac{1}{2} ki te x-y+\frac{1}{2}, ka \left(x-y+\frac{1}{2}\right)^{2}.

$$\left(x-y+\frac{1}{2}\right)^{2}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Pūrua x-y+\frac{1}{2}.

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x-y\right)^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-\left(x^{2}-2xy+y^{2}\right)+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x^{2}-2xy+x+y^{2}-y+\frac{1}{4}-x^{2}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$-2xy+x+y^{2}-y+\frac{1}{4}+2xy-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Pahekotia te -2xy me 2xy, ka 0.

$$x+y^{2}-y+\frac{1}{4}-y^{2}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(\frac{1}{3}x^{2}-\frac{3}{2}\right)^{3}.

$$x-y+\frac{1}{4}+\frac{1}{27}\left(x^{2}\right)^{3}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 3 kia riro ai te 6.

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}\left(x^{2}\right)^{2}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

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

$$x-y+\frac{1}{4}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{27}{8}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Tangohia te \frac{27}{8} i te \frac{1}{4}, ka -\frac{25}{8}.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-x^{2}\left(\frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te \frac{1}{27}x^{4}-\frac{1}{2}x^{2}+\frac{9}{4}.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\left(\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}\right)$$

Hei kimi i te tauaro o \frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}, kimihia te tauaro o ia taurangi.

$$x-y-\frac{25}{8}+\frac{1}{27}x^{6}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}-\frac{1}{27}x^{6}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

Pahekotia te \frac{1}{27}x^{6} me -\frac{1}{27}x^{6}, ka 0.

$$x-y-\frac{25}{8}-\frac{1}{2}x^{4}+\frac{9}{4}x^{2}+\frac{1}{2}x^{4}-\frac{9}{4}x^{2}$$

Pahekotia te -\frac{1}{2}x^{4} me \frac{1}{2}x^{4}, ka 0.

$$x-y-\frac{25}{8}+\frac{9}{4}x^{2}-\frac{9}{4}x^{2}$$

Pahekotia te \frac{9}{4}x^{2} me -\frac{9}{4}x^{2}, ka 0.

$$x-y-\frac{25}{8}$$