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

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

Baholash

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

Yechim qadamlari

2x+\frac{1}{3}y ifodaning har bir elementini x-3y ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

y^{2} hosil qilish uchun y va y ni ko'paytirish.

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

-\frac{17}{3}xy ni olish uchun -6xy va \frac{1}{3}yx ni birlashtirish.

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

\frac{-3}{3} hosil qilish uchun \frac{1}{3} va -3 ni ko'paytirish.

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

-1 ni olish uchun -3 ni 3 ga bo‘ling.

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

2x+y ifodaning har bir elementini \frac{1}{2}x-y ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

2 va 2 ni qisqartiring.

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

-\frac{3}{2}xy ni olish uchun -2xy va y\times \frac{1}{2}x ni birlashtirish.

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

x^{2}-\frac{3}{2}xy-y^{2} teskarisini topish uchun har birining teskarisini toping.

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

-\frac{3}{2}xy ning teskarisi \frac{3}{2}xy ga teng.

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

-y^{2} ning teskarisi y^{2} ga teng.

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

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

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

-\frac{25}{6}xy ni olish uchun -\frac{17}{3}xy va \frac{3}{2}xy ni birlashtirish.

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

0 ni olish uchun -y^{2} va y^{2} ni birlashtirish.

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

Kengaytirish

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

Yechim qadamlari

2x+\frac{1}{3}y ifodaning har bir elementini x-3y ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

y^{2} hosil qilish uchun y va y ni ko'paytirish.

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

-\frac{17}{3}xy ni olish uchun -6xy va \frac{1}{3}yx ni birlashtirish.

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

\frac{-3}{3} hosil qilish uchun \frac{1}{3} va -3 ni ko'paytirish.

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

-1 ni olish uchun -3 ni 3 ga bo‘ling.

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

2x+y ifodaning har bir elementini \frac{1}{2}x-y ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

2 va 2 ni qisqartiring.

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

-\frac{3}{2}xy ni olish uchun -2xy va y\times \frac{1}{2}x ni birlashtirish.

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

x^{2}-\frac{3}{2}xy-y^{2} teskarisini topish uchun har birining teskarisini toping.

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

-\frac{3}{2}xy ning teskarisi \frac{3}{2}xy ga teng.

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

-y^{2} ning teskarisi y^{2} ga teng.

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

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

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

-\frac{25}{6}xy ni olish uchun -\frac{17}{3}xy va \frac{3}{2}xy ni birlashtirish.

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

0 ni olish uchun -y^{2} va y^{2} ni birlashtirish.

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