Réitigh (2x+1/3y)(x-3y)-(2x+y)(1/2x-y)=

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

Luacháil

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

Céimeanna Réitigh

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2x+\frac{1}{3}y a iolrú faoi gach téarma de x-3y.

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

Méadaigh y agus y chun y^{2} a fháil.

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

Comhcheangail -6xy agus \frac{1}{3}yx chun -\frac{17}{3}xy a fháil.

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

Méadaigh \frac{1}{3} agus -3 chun \frac{-3}{3} a fháil.

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

Roinn -3 faoi 3 chun -1 a fháil.

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

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2x+y a iolrú faoi gach téarma de \frac{1}{2}x-y.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Cealaigh 2 agus 2.

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

Comhcheangail -2xy agus y\times \frac{1}{2}x chun -\frac{3}{2}xy a fháil.

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

Chun an mhalairt ar x^{2}-\frac{3}{2}xy-y^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Tá \frac{3}{2}xy urchomhairleach le -\frac{3}{2}xy.

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

Tá y^{2} urchomhairleach le -y^{2}.

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

Comhcheangail 2x^{2} agus -x^{2} chun x^{2} a fháil.

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

Comhcheangail -\frac{17}{3}xy agus \frac{3}{2}xy chun -\frac{25}{6}xy a fháil.

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

Comhcheangail -y^{2} agus y^{2} chun 0 a fháil.

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

Fairsingigh

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

Céimeanna Réitigh

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2x+\frac{1}{3}y a iolrú faoi gach téarma de x-3y.

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

Méadaigh y agus y chun y^{2} a fháil.

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

Comhcheangail -6xy agus \frac{1}{3}yx chun -\frac{17}{3}xy a fháil.

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

Méadaigh \frac{1}{3} agus -3 chun \frac{-3}{3} a fháil.

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

Roinn -3 faoi 3 chun -1 a fháil.

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

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2x+y a iolrú faoi gach téarma de \frac{1}{2}x-y.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Cealaigh 2 agus 2.

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

Comhcheangail -2xy agus y\times \frac{1}{2}x chun -\frac{3}{2}xy a fháil.

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

Chun an mhalairt ar x^{2}-\frac{3}{2}xy-y^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Tá \frac{3}{2}xy urchomhairleach le -\frac{3}{2}xy.

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

Tá y^{2} urchomhairleach le -y^{2}.

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

Comhcheangail 2x^{2} agus -x^{2} chun x^{2} a fháil.

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

Comhcheangail -\frac{17}{3}xy agus \frac{3}{2}xy chun -\frac{25}{6}xy a fháil.

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

Comhcheangail -y^{2} agus y^{2} chun 0 a fháil.

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