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

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

Izrēķināt

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

Atrisinājuma darbības

Izmantojiet distributīvo īpašību, katru 2x+\frac{1}{3}y locekli reizinot ar katru x-3y locekli.

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

Reiziniet y un y, lai iegūtu y^{2}.

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

Savelciet -6xy un \frac{1}{3}yx, lai iegūtu -\frac{17}{3}xy.

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

Reiziniet \frac{1}{3} un -3, lai iegūtu \frac{-3}{3}.

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

Daliet -3 ar 3, lai iegūtu -1.

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

Izmantojiet distributīvo īpašību, katru 2x+y locekli reizinot ar katru \frac{1}{2}x-y locekli.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Saīsiniet 2 un 2.

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

Savelciet -2xy un y\times \frac{1}{2}x, lai iegūtu -\frac{3}{2}xy.

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

Lai atrastu x^{2}-\frac{3}{2}xy-y^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.

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

Skaitļa -\frac{3}{2}xy pretstats ir \frac{3}{2}xy.

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

Skaitļa -y^{2} pretstats ir y^{2}.

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

Savelciet 2x^{2} un -x^{2}, lai iegūtu x^{2}.

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

Savelciet -\frac{17}{3}xy un \frac{3}{2}xy, lai iegūtu -\frac{25}{6}xy.

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

Savelciet -y^{2} un y^{2}, lai iegūtu 0.

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

Paplašināt

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

Atrisinājuma darbības

Izmantojiet distributīvo īpašību, katru 2x+\frac{1}{3}y locekli reizinot ar katru x-3y locekli.

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

Reiziniet y un y, lai iegūtu y^{2}.

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

Savelciet -6xy un \frac{1}{3}yx, lai iegūtu -\frac{17}{3}xy.

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

Reiziniet \frac{1}{3} un -3, lai iegūtu \frac{-3}{3}.

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

Daliet -3 ar 3, lai iegūtu -1.

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

Izmantojiet distributīvo īpašību, katru 2x+y locekli reizinot ar katru \frac{1}{2}x-y locekli.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Saīsiniet 2 un 2.

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

Savelciet -2xy un y\times \frac{1}{2}x, lai iegūtu -\frac{3}{2}xy.

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

Lai atrastu x^{2}-\frac{3}{2}xy-y^{2} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.

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

Skaitļa -\frac{3}{2}xy pretstats ir \frac{3}{2}xy.

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

Skaitļa -y^{2} pretstats ir y^{2}.

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

Savelciet 2x^{2} un -x^{2}, lai iegūtu x^{2}.

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

Savelciet -\frac{17}{3}xy un \frac{3}{2}xy, lai iegūtu -\frac{25}{6}xy.

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

Savelciet -y^{2} un y^{2}, lai iegūtu 0.

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