3[(4+3b)^2+2]+[2*(a-b)^2]= eching

$$3 [ ( 4 + 3 b ) ^ { 2 } + 2 ] + [ 2 \cdot ( a - b ) ^ { 2 } ] =$$

Baholash

$$2\left(a-b\right)^{2}+3\left(3b+4\right)^{2}+6$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(4+3b\right)^{2} kengaytirilishi uchun ishlating.

$$3\left(16+24b+9b^{2}+2\right)+2\left(a-b\right)^{2}$$

18 olish uchun 16 va 2'ni qo'shing.

$$3\left(18+24b+9b^{2}\right)+2\left(a-b\right)^{2}$$

3 ga 18+24b+9b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$54+72b+27b^{2}+2\left(a-b\right)^{2}$$

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

$$54+72b+27b^{2}+2\left(a^{2}-2ab+b^{2}\right)$$

2 ga a^{2}-2ab+b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$54+72b+27b^{2}+2a^{2}-4ab+2b^{2}$$

29b^{2} ni olish uchun 27b^{2} va 2b^{2} ni birlashtirish.

$$54+72b+29b^{2}+2a^{2}-4ab$$

Kengaytirish

$$2a^{2}-4ab+29b^{2}+72b+54$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(4+3b\right)^{2} kengaytirilishi uchun ishlating.

$$3\left(16+24b+9b^{2}+2\right)+2\left(a-b\right)^{2}$$

18 olish uchun 16 va 2'ni qo'shing.

$$3\left(18+24b+9b^{2}\right)+2\left(a-b\right)^{2}$$

3 ga 18+24b+9b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$54+72b+27b^{2}+2\left(a-b\right)^{2}$$

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

$$54+72b+27b^{2}+2\left(a^{2}-2ab+b^{2}\right)$$

2 ga a^{2}-2ab+b^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$54+72b+27b^{2}+2a^{2}-4ab+2b^{2}$$

29b^{2} ni olish uchun 27b^{2} va 2b^{2} ni birlashtirish.

$$54+72b+29b^{2}+2a^{2}-4ab$$