=2(x+1)^3+4(x+1)^2-3(x+1)+6 eching

$$= 2 ( x + 1 ) ^ { 3 } + 4 ( x + 1 ) ^ { 2 } - 3 ( x + 1 ) + 6$$

Baholash

$$2x^{3}+10x^{2}+11x+9$$

Yechim qadamlari

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

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

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

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

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

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

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

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

10x^{2} ni olish uchun 6x^{2} va 4x^{2} ni birlashtirish.

$$2x^{3}+10x^{2}+6x+2+8x+4-3\left(x+1\right)+6$$

14x ni olish uchun 6x va 8x ni birlashtirish.

$$2x^{3}+10x^{2}+14x+2+4-3\left(x+1\right)+6$$

6 olish uchun 2 va 4'ni qo'shing.

$$2x^{3}+10x^{2}+14x+6-3\left(x+1\right)+6$$

-3 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{3}+10x^{2}+14x+6-3x-3+6$$

11x ni olish uchun 14x va -3x ni birlashtirish.

$$2x^{3}+10x^{2}+11x+6-3+6$$

3 olish uchun 6 dan 3 ni ayirish.

$$2x^{3}+10x^{2}+11x+3+6$$

9 olish uchun 3 va 6'ni qo'shing.

$$2x^{3}+10x^{2}+11x+9$$

Kengaytirish

$$2x^{3}+10x^{2}+11x+9$$

Yechim qadamlari

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

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

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

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

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

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

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

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

10x^{2} ni olish uchun 6x^{2} va 4x^{2} ni birlashtirish.

$$2x^{3}+10x^{2}+6x+2+8x+4-3\left(x+1\right)+6$$

14x ni olish uchun 6x va 8x ni birlashtirish.

$$2x^{3}+10x^{2}+14x+2+4-3\left(x+1\right)+6$$

6 olish uchun 2 va 4'ni qo'shing.

$$2x^{3}+10x^{2}+14x+6-3\left(x+1\right)+6$$

-3 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{3}+10x^{2}+14x+6-3x-3+6$$

11x ni olish uchun 14x va -3x ni birlashtirish.

$$2x^{3}+10x^{2}+11x+6-3+6$$

3 olish uchun 6 dan 3 ni ayirish.

$$2x^{3}+10x^{2}+11x+3+6$$

9 olish uchun 3 va 6'ni qo'shing.

$$2x^{3}+10x^{2}+11x+9$$