left(x-2yright)^3-xleft(x-2yright)left(x+2yright)+2xyleft(3x+4yright)-left(-2yright)^3 eching

$${ \left(x-2y \right) }^{ 3 } -x \left( x-2y \right) \left( x+2y \right) +2xy \left( 3x+4y \right) - { \left(-2y \right) }^{ 3 }$$

Baholash

$$24xy^{2}$$

Yechim qadamlari

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

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-x\left(x-2y\right)\left(x+2y\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

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

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-\left(x^{2}-2xy\right)\left(x+2y\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

x^{2}-2xy ga x+2y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-\left(x^{3}-4xy^{2}\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

x^{3}-4xy^{2} teskarisini topish uchun har birining teskarisini toping.

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-x^{3}+4xy^{2}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

0 ni olish uchun x^{3} va -x^{3} ni birlashtirish.

$$-6x^{2}y+12xy^{2}-8y^{3}+4xy^{2}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

16xy^{2} ni olish uchun 12xy^{2} va 4xy^{2} ni birlashtirish.

$$-6x^{2}y+16xy^{2}-8y^{3}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

2xy ga 3x+4y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-6x^{2}y+16xy^{2}-8y^{3}+6x^{2}y+8xy^{2}-\left(-2y\right)^{3}$$

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

$$16xy^{2}-8y^{3}+8xy^{2}-\left(-2y\right)^{3}$$

24xy^{2} ni olish uchun 16xy^{2} va 8xy^{2} ni birlashtirish.

$$24xy^{2}-8y^{3}-\left(-2y\right)^{3}$$

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

$$24xy^{2}-8y^{3}-\left(-2\right)^{3}y^{3}$$

3 daraja ko‘rsatkichini -2 ga hisoblang va -8 ni qiymatni oling.

$$24xy^{2}-8y^{3}-\left(-8y^{3}\right)$$

-8y^{3} ning teskarisi 8y^{3} ga teng.

$$24xy^{2}-8y^{3}+8y^{3}$$

0 ni olish uchun -8y^{3} va 8y^{3} ni birlashtirish.

$$24xy^{2}$$

Kengaytirish

$$24xy^{2}$$

Yechim qadamlari

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

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-x\left(x-2y\right)\left(x+2y\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

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

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-\left(x^{2}-2xy\right)\left(x+2y\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

x^{2}-2xy ga x+2y ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-\left(x^{3}-4xy^{2}\right)+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

x^{3}-4xy^{2} teskarisini topish uchun har birining teskarisini toping.

$$x^{3}-6x^{2}y+12xy^{2}-8y^{3}-x^{3}+4xy^{2}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

0 ni olish uchun x^{3} va -x^{3} ni birlashtirish.

$$-6x^{2}y+12xy^{2}-8y^{3}+4xy^{2}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

16xy^{2} ni olish uchun 12xy^{2} va 4xy^{2} ni birlashtirish.

$$-6x^{2}y+16xy^{2}-8y^{3}+2xy\left(3x+4y\right)-\left(-2y\right)^{3}$$

2xy ga 3x+4y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-6x^{2}y+16xy^{2}-8y^{3}+6x^{2}y+8xy^{2}-\left(-2y\right)^{3}$$

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

$$16xy^{2}-8y^{3}+8xy^{2}-\left(-2y\right)^{3}$$

24xy^{2} ni olish uchun 16xy^{2} va 8xy^{2} ni birlashtirish.

$$24xy^{2}-8y^{3}-\left(-2y\right)^{3}$$

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

$$24xy^{2}-8y^{3}-\left(-2\right)^{3}y^{3}$$

3 daraja ko‘rsatkichini -2 ga hisoblang va -8 ni qiymatni oling.

$$24xy^{2}-8y^{3}-\left(-8y^{3}\right)$$

-8y^{3} ning teskarisi 8y^{3} ga teng.

$$24xy^{2}-8y^{3}+8y^{3}$$

0 ni olish uchun -8y^{3} va 8y^{3} ni birlashtirish.

$$24xy^{2}$$