(y+3x)(3x-y)-(2y-x)(3y+x) eching

$$( y + 3 x ) ( 3 x - y ) - ( 2 y - x ) ( 3 y + x )$$

Baholash

$$10x^{2}+xy-7y^{2}$$

Yechim qadamlari

Hisoblang: \left(y+3x\right)\left(3x-y\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(3x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

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

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

$$9x^{2}-y^{2}-\left(6y^{2}+2yx-3xy-x^{2}\right)$$

-yx ni olish uchun 2yx va -3xy ni birlashtirish.

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

6y^{2}-yx-x^{2} teskarisini topish uchun har birining teskarisini toping.

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

-yx ning teskarisi yx ga teng.

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

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

$$9x^{2}-y^{2}-6y^{2}+yx+x^{2}$$

-7y^{2} ni olish uchun -y^{2} va -6y^{2} ni birlashtirish.

$$9x^{2}-7y^{2}+yx+x^{2}$$

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

$$10x^{2}-7y^{2}+yx$$

Kengaytirish

$$10x^{2}+xy-7y^{2}$$

Yechim qadamlari

Hisoblang: \left(y+3x\right)\left(3x-y\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(3x\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

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

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

$$9x^{2}-y^{2}-\left(6y^{2}+2yx-3xy-x^{2}\right)$$

-yx ni olish uchun 2yx va -3xy ni birlashtirish.

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

6y^{2}-yx-x^{2} teskarisini topish uchun har birining teskarisini toping.

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

-yx ning teskarisi yx ga teng.

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

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

$$9x^{2}-y^{2}-6y^{2}+yx+x^{2}$$

-7y^{2} ni olish uchun -y^{2} va -6y^{2} ni birlashtirish.

$$9x^{2}-7y^{2}+yx+x^{2}$$

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

$$10x^{2}-7y^{2}+yx$$