=(2x^2+1)^2+3(2x^2+1) eching

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

Baholash

$$4x^{4}+10x^{2}+4$$

Yechim qadamlari

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

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

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

$$4x^{4}+4x^{2}+1+6x^{2}+3$$

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

$$4x^{4}+10x^{2}+1+3$$

4 olish uchun 1 va 3'ni qo'shing.

$$4x^{4}+10x^{2}+4$$

Kengaytirish

$$4x^{4}+10x^{2}+4$$

Yechim qadamlari

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

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

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

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

$$4x^{4}+4x^{2}+1+6x^{2}+3$$

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

$$4x^{4}+10x^{2}+1+3$$

4 olish uchun 1 va 3'ni qo'shing.

$$4x^{4}+10x^{2}+4$$