2(2a+3)^3-3(a-2)^3 eching

$$2 ( 2 a + 3 ) ^ { 3 } - 3 ( a - 2 ) ^ { 3 }$$

Kengaytirish

$$13a^{3}+90a^{2}+72a+78$$

Yechim qadamlari

\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} binom teoremasini \left(2a+3\right)^{3} kengaytirilishi uchun ishlating.

$$2\left(8a^{3}+36a^{2}+54a+27\right)-3\left(a-2\right)^{3}$$

2 ga 8a^{3}+36a^{2}+54a+27 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16a^{3}+72a^{2}+108a+54-3\left(a-2\right)^{3}$$

\left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} binom teoremasini \left(a-2\right)^{3} kengaytirilishi uchun ishlating.

$$16a^{3}+72a^{2}+108a+54-3\left(a^{3}-6a^{2}+12a-8\right)$$

-3 ga a^{3}-6a^{2}+12a-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16a^{3}+72a^{2}+108a+54-3a^{3}+18a^{2}-36a+24$$

13a^{3} ni olish uchun 16a^{3} va -3a^{3} ni birlashtirish.

$$13a^{3}+72a^{2}+108a+54+18a^{2}-36a+24$$

90a^{2} ni olish uchun 72a^{2} va 18a^{2} ni birlashtirish.

$$13a^{3}+90a^{2}+108a+54-36a+24$$

72a ni olish uchun 108a va -36a ni birlashtirish.

$$13a^{3}+90a^{2}+72a+54+24$$

78 olish uchun 54 va 24'ni qo'shing.

$$13a^{3}+90a^{2}+72a+78$$

Baholash

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

Yechim qadamlari

\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} binom teoremasini \left(2a+3\right)^{3} kengaytirilishi uchun ishlating.

$$2\left(8a^{3}+36a^{2}+54a+27\right)-3\left(a-2\right)^{3}$$

2 ga 8a^{3}+36a^{2}+54a+27 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16a^{3}+72a^{2}+108a+54-3\left(a-2\right)^{3}$$

\left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} binom teoremasini \left(a-2\right)^{3} kengaytirilishi uchun ishlating.

$$16a^{3}+72a^{2}+108a+54-3\left(a^{3}-6a^{2}+12a-8\right)$$

-3 ga a^{3}-6a^{2}+12a-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16a^{3}+72a^{2}+108a+54-3a^{3}+18a^{2}-36a+24$$

13a^{3} ni olish uchun 16a^{3} va -3a^{3} ni birlashtirish.

$$13a^{3}+72a^{2}+108a+54+18a^{2}-36a+24$$

90a^{2} ni olish uchun 72a^{2} va 18a^{2} ni birlashtirish.

$$13a^{3}+90a^{2}+108a+54-36a+24$$

72a ni olish uchun 108a va -36a ni birlashtirish.

$$13a^{3}+90a^{2}+72a+54+24$$

78 olish uchun 54 va 24'ni qo'shing.

$$13a^{3}+90a^{2}+72a+78$$