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

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

Ovrednoti

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

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost 2x+\frac{1}{3}y z vsako vrednostjo x-3y.

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

Pomnožite y in y, da dobite y^{2}.

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

Združite -6xy in \frac{1}{3}yx, da dobite -\frac{17}{3}xy.

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

Pomnožite \frac{1}{3} in -3, da dobite \frac{-3}{3}.

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

Delite -3 s/z 3, da dobite -1.

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

Uporabite distributivnost tako, da pomnožite vsako vrednost 2x+y z vsako vrednostjo \frac{1}{2}x-y.

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

Pomnožite x in x, da dobite x^{2}.

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

Okrajšaj 2 in 2.

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

Združite -2xy in y\times \frac{1}{2}x, da dobite -\frac{3}{2}xy.

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

Če želite poiskati nasprotno vrednost za x^{2}-\frac{3}{2}xy-y^{2}, poiščite nasprotno vrednost vsakega izraza.

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

Nasprotna vrednost -\frac{3}{2}xy je \frac{3}{2}xy.

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

Nasprotna vrednost -y^{2} je y^{2}.

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

Združite 2x^{2} in -x^{2}, da dobite x^{2}.

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

Združite -\frac{17}{3}xy in \frac{3}{2}xy, da dobite -\frac{25}{6}xy.

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

Združite -y^{2} in y^{2}, da dobite 0.

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

Razširi

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

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost 2x+\frac{1}{3}y z vsako vrednostjo x-3y.

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

Pomnožite y in y, da dobite y^{2}.

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

Združite -6xy in \frac{1}{3}yx, da dobite -\frac{17}{3}xy.

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

Pomnožite \frac{1}{3} in -3, da dobite \frac{-3}{3}.

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

Delite -3 s/z 3, da dobite -1.

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

Uporabite distributivnost tako, da pomnožite vsako vrednost 2x+y z vsako vrednostjo \frac{1}{2}x-y.

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

Pomnožite x in x, da dobite x^{2}.

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

Okrajšaj 2 in 2.

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

Združite -2xy in y\times \frac{1}{2}x, da dobite -\frac{3}{2}xy.

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

Če želite poiskati nasprotno vrednost za x^{2}-\frac{3}{2}xy-y^{2}, poiščite nasprotno vrednost vsakega izraza.

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

Nasprotna vrednost -\frac{3}{2}xy je \frac{3}{2}xy.

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

Nasprotna vrednost -y^{2} je y^{2}.

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

Združite 2x^{2} in -x^{2}, da dobite x^{2}.

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

Združite -\frac{17}{3}xy in \frac{3}{2}xy, da dobite -\frac{25}{6}xy.

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

Združite -y^{2} in y^{2}, da dobite 0.

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