(2y-1)^3-3(2y-1)^2 eching

$$( 2 y - 1 ) ^ { 3 } - 3 ( 2 y - 1 ) ^ { 2 }$$

Baholash

$$2\left(y-2\right)\left(2y-1\right)^{2}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(2y-1\right)^{3} kengaytirilishi uchun ishlating.

$$8y^{3}-12y^{2}+6y-1-3\left(2y-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2y-1\right)^{2} kengaytirilishi uchun ishlating.

$$8y^{3}-12y^{2}+6y-1-3\left(4y^{2}-4y+1\right)$$

-3 ga 4y^{2}-4y+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8y^{3}-12y^{2}+6y-1-12y^{2}+12y-3$$

-24y^{2} ni olish uchun -12y^{2} va -12y^{2} ni birlashtirish.

$$8y^{3}-24y^{2}+6y-1+12y-3$$

18y ni olish uchun 6y va 12y ni birlashtirish.

$$8y^{3}-24y^{2}+18y-1-3$$

-4 olish uchun -1 dan 3 ni ayirish.

$$8y^{3}-24y^{2}+18y-4$$

Kengaytirish

$$8y^{3}-24y^{2}+18y-4$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(2y-1\right)^{3} kengaytirilishi uchun ishlating.

$$8y^{3}-12y^{2}+6y-1-3\left(2y-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2y-1\right)^{2} kengaytirilishi uchun ishlating.

$$8y^{3}-12y^{2}+6y-1-3\left(4y^{2}-4y+1\right)$$

-3 ga 4y^{2}-4y+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8y^{3}-12y^{2}+6y-1-12y^{2}+12y-3$$

-24y^{2} ni olish uchun -12y^{2} va -12y^{2} ni birlashtirish.

$$8y^{3}-24y^{2}+6y-1+12y-3$$

18y ni olish uchun 6y va 12y ni birlashtirish.

$$8y^{3}-24y^{2}+18y-1-3$$

-4 olish uchun -1 dan 3 ni ayirish.

$$8y^{3}-24y^{2}+18y-4$$