2(y-3x)^2+2(y+2x)(y-2x)-9x^2-2xy-(2y-x)^2 eching

$$2 ( y - 3 x ) ^ { 2 } + 2 ( y + 2 x ) ( y - 2 x ) - 9 x ^ { 2 } - 2 x y - ( 2 y - x ) ^ { 2 }$$

Baholash

$$-10xy$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(y-3x\right)^{2} kengaytirilishi uchun ishlating.

$$2\left(y^{2}-6yx+9x^{2}\right)+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2 ga y^{2}-6yx+9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2y^{2}-12yx+18x^{2}+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2 ga y+2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2y^{2}-12yx+18x^{2}+\left(2y+4x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2y+4x ga y-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2y^{2}-12yx+18x^{2}+2y^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

4y^{2} ni olish uchun 2y^{2} va 2y^{2} ni birlashtirish.

$$4y^{2}-12yx+18x^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

10x^{2} ni olish uchun 18x^{2} va -8x^{2} ni birlashtirish.

$$4y^{2}-12yx+10x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

x^{2} ni olish uchun 10x^{2} va -9x^{2} ni birlashtirish.

$$4y^{2}-12yx+x^{2}-2xy-\left(2y-x\right)^{2}$$

-14yx ni olish uchun -12yx va -2xy ni birlashtirish.

$$4y^{2}-14yx+x^{2}-\left(2y-x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2y-x\right)^{2} kengaytirilishi uchun ishlating.

$$4y^{2}-14yx+x^{2}-\left(4y^{2}-4yx+x^{2}\right)$$

4y^{2}-4yx+x^{2} teskarisini topish uchun har birining teskarisini toping.

$$4y^{2}-14yx+x^{2}-4y^{2}+4yx-x^{2}$$

0 ni olish uchun 4y^{2} va -4y^{2} ni birlashtirish.

$$-14yx+x^{2}+4yx-x^{2}$$

-10yx ni olish uchun -14yx va 4yx ni birlashtirish.

$$-10yx+x^{2}-x^{2}$$

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

$$-10yx$$

Kengaytirish

$$-10xy$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(y-3x\right)^{2} kengaytirilishi uchun ishlating.

$$2\left(y^{2}-6yx+9x^{2}\right)+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2 ga y^{2}-6yx+9x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2y^{2}-12yx+18x^{2}+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2 ga y+2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2y^{2}-12yx+18x^{2}+\left(2y+4x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

2y+4x ga y-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2y^{2}-12yx+18x^{2}+2y^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

4y^{2} ni olish uchun 2y^{2} va 2y^{2} ni birlashtirish.

$$4y^{2}-12yx+18x^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

10x^{2} ni olish uchun 18x^{2} va -8x^{2} ni birlashtirish.

$$4y^{2}-12yx+10x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

x^{2} ni olish uchun 10x^{2} va -9x^{2} ni birlashtirish.

$$4y^{2}-12yx+x^{2}-2xy-\left(2y-x\right)^{2}$$

-14yx ni olish uchun -12yx va -2xy ni birlashtirish.

$$4y^{2}-14yx+x^{2}-\left(2y-x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2y-x\right)^{2} kengaytirilishi uchun ishlating.

$$4y^{2}-14yx+x^{2}-\left(4y^{2}-4yx+x^{2}\right)$$

4y^{2}-4yx+x^{2} teskarisini topish uchun har birining teskarisini toping.

$$4y^{2}-14yx+x^{2}-4y^{2}+4yx-x^{2}$$

0 ni olish uchun 4y^{2} va -4y^{2} ni birlashtirish.

$$-14yx+x^{2}+4yx-x^{2}$$

-10yx ni olish uchun -14yx va 4yx ni birlashtirish.

$$-10yx+x^{2}-x^{2}$$

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

$$-10yx$$