Whakaoti i te (2x+1/3y)(x-3y)-(2x+y)(1/2x-y)=

$$( 2 x + \frac { 1 } { 3 } y ) ( x - 3 y ) - ( 2 x + y ) ( \frac { 1 } { 2 } x - y ) =$$

Aromātai

$$-\frac{25xy}{6}+x^{2}$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+\frac{1}{3}y ki ia tau o x-3y.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y\left(-3\right)y-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakareatia te y ki te y, ka y^{2}.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Pahekotia te -6xy me \frac{1}{3}yx, ka -\frac{17}{3}xy.

$$2x^{2}-\frac{17}{3}xy+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakareatia te \frac{1}{3} ki te -3, ka \frac{-3}{3}.

$$2x^{2}-\frac{17}{3}xy+\frac{-3}{3}y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakawehea te -3 ki te 3, kia riro ko -1.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+y ki ia tau o \frac{1}{2}x-y.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x\times \frac{1}{2}x-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Whakareatia te x ki te x, ka x^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x^{2}\times \frac{1}{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Me whakakore te 2 me te 2.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Pahekotia te -2xy me y\times \frac{1}{2}x, ka -\frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-\frac{3}{2}xy-y^{2}\right)$$

Hei kimi i te tauaro o x^{2}-\frac{3}{2}xy-y^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}-\left(-\frac{3}{2}xy\right)-\left(-y^{2}\right)$$

Ko te tauaro o -\frac{3}{2}xy ko \frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy-\left(-y^{2}\right)$$

Ko te tauaro o -y^{2} ko y^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy+y^{2}$$

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

$$x^{2}-\frac{17}{3}xy-y^{2}+\frac{3}{2}xy+y^{2}$$

Pahekotia te -\frac{17}{3}xy me \frac{3}{2}xy, ka -\frac{25}{6}xy.

$$x^{2}-\frac{25}{6}xy-y^{2}+y^{2}$$

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

$$x^{2}-\frac{25}{6}xy$$

Whakaroha

$$-\frac{25xy}{6}+x^{2}$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+\frac{1}{3}y ki ia tau o x-3y.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y\left(-3\right)y-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakareatia te y ki te y, ka y^{2}.

$$2x^{2}-6xy+\frac{1}{3}yx+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Pahekotia te -6xy me \frac{1}{3}yx, ka -\frac{17}{3}xy.

$$2x^{2}-\frac{17}{3}xy+\frac{1}{3}y^{2}\left(-3\right)-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakareatia te \frac{1}{3} ki te -3, ka \frac{-3}{3}.

$$2x^{2}-\frac{17}{3}xy+\frac{-3}{3}y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Whakawehea te -3 ki te 3, kia riro ko -1.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x+y\right)\left(\frac{1}{2}x-y\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+y ki ia tau o \frac{1}{2}x-y.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x\times \frac{1}{2}x-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Whakareatia te x ki te x, ka x^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(2x^{2}\times \frac{1}{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Me whakakore te 2 me te 2.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-2xy+y\times \frac{1}{2}x-y^{2}\right)$$

Pahekotia te -2xy me y\times \frac{1}{2}x, ka -\frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-\left(x^{2}-\frac{3}{2}xy-y^{2}\right)$$

Hei kimi i te tauaro o x^{2}-\frac{3}{2}xy-y^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}-\left(-\frac{3}{2}xy\right)-\left(-y^{2}\right)$$

Ko te tauaro o -\frac{3}{2}xy ko \frac{3}{2}xy.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy-\left(-y^{2}\right)$$

Ko te tauaro o -y^{2} ko y^{2}.

$$2x^{2}-\frac{17}{3}xy-y^{2}-x^{2}+\frac{3}{2}xy+y^{2}$$

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

$$x^{2}-\frac{17}{3}xy-y^{2}+\frac{3}{2}xy+y^{2}$$

Pahekotia te -\frac{17}{3}xy me \frac{3}{2}xy, ka -\frac{25}{6}xy.

$$x^{2}-\frac{25}{6}xy-y^{2}+y^{2}$$

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

$$x^{2}-\frac{25}{6}xy$$