left(3x^2+1right)^3 eching

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

Kengaytirish

$$27x^{6}+27x^{4}+9x^{2}+1$$

Yechim qadamlari

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

$$27\left(x^{2}\right)^{3}+27\left(x^{2}\right)^{2}+9x^{2}+1$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$27x^{6}+27\left(x^{2}\right)^{2}+9x^{2}+1$$

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

$$27x^{6}+27x^{4}+9x^{2}+1$$

Baholash

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

Yechim qadamlari

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

$$27\left(x^{2}\right)^{3}+27\left(x^{2}\right)^{2}+9x^{2}+1$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$27x^{6}+27\left(x^{2}\right)^{2}+9x^{2}+1$$

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

$$27x^{6}+27x^{4}+9x^{2}+1$$