(4-6x)^3-4(4-6x)^2+7(4-6x)-1 eching

$$( 4 - 6 x ) ^ { 3 } - 4 ( 4 - 6 x ) ^ { 2 } + 7 ( 4 - 6 x ) - 1$$

Baholash

$$27-138x+288x^{2}-216x^{3}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(4-6x\right)^{3} kengaytirilishi uchun ishlating.

$$64-288x+432x^{2}-216x^{3}-4\left(4-6x\right)^{2}+7\left(4-6x\right)-1$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-6x\right)^{2} kengaytirilishi uchun ishlating.

$$64-288x+432x^{2}-216x^{3}-4\left(16-48x+36x^{2}\right)+7\left(4-6x\right)-1$$

-4 ga 16-48x+36x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$64-288x+432x^{2}-216x^{3}-64+192x-144x^{2}+7\left(4-6x\right)-1$$

0 olish uchun 64 dan 64 ni ayirish.

$$-288x+432x^{2}-216x^{3}+192x-144x^{2}+7\left(4-6x\right)-1$$

-96x ni olish uchun -288x va 192x ni birlashtirish.

$$-96x+432x^{2}-216x^{3}-144x^{2}+7\left(4-6x\right)-1$$

288x^{2} ni olish uchun 432x^{2} va -144x^{2} ni birlashtirish.

$$-96x+288x^{2}-216x^{3}+7\left(4-6x\right)-1$$

7 ga 4-6x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-96x+288x^{2}-216x^{3}+28-42x-1$$

-138x ni olish uchun -96x va -42x ni birlashtirish.

$$-138x+288x^{2}-216x^{3}+28-1$$

27 olish uchun 28 dan 1 ni ayirish.

$$-138x+288x^{2}-216x^{3}+27$$

Kengaytirish

$$27-138x+288x^{2}-216x^{3}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(4-6x\right)^{3} kengaytirilishi uchun ishlating.

$$64-288x+432x^{2}-216x^{3}-4\left(4-6x\right)^{2}+7\left(4-6x\right)-1$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-6x\right)^{2} kengaytirilishi uchun ishlating.

$$64-288x+432x^{2}-216x^{3}-4\left(16-48x+36x^{2}\right)+7\left(4-6x\right)-1$$

-4 ga 16-48x+36x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$64-288x+432x^{2}-216x^{3}-64+192x-144x^{2}+7\left(4-6x\right)-1$$

0 olish uchun 64 dan 64 ni ayirish.

$$-288x+432x^{2}-216x^{3}+192x-144x^{2}+7\left(4-6x\right)-1$$

-96x ni olish uchun -288x va 192x ni birlashtirish.

$$-96x+432x^{2}-216x^{3}-144x^{2}+7\left(4-6x\right)-1$$

288x^{2} ni olish uchun 432x^{2} va -144x^{2} ni birlashtirish.

$$-96x+288x^{2}-216x^{3}+7\left(4-6x\right)-1$$

7 ga 4-6x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-96x+288x^{2}-216x^{3}+28-42x-1$$

-138x ni olish uchun -96x va -42x ni birlashtirish.

$$-138x+288x^{2}-216x^{3}+28-1$$

27 olish uchun 28 dan 1 ni ayirish.

$$-138x+288x^{2}-216x^{3}+27$$